simulation, design and validation of a solid oxide …

SIMULATION, DESIGN AND VALIDATION OF A SOLID OXIDE FUEL CELL

POWERED PROPULSION SYSTEM FOR AN UNMANNED AERIAL VEHICLE

by

Peter Allan Lindahl

A thesis submitted in partial fulfillmentof the requirements for the degree

of

Master of Science

in

Electrical Engineering

MONTANA STATE UNIVERSITYBozeman, Montana

April, 2009

© Copyright

by

Peter Allan Lindahl

and portions by

The Institute of Electrical and Electronics Engineers

2009

All Rights Reserved

Unless otherwise indicated, this information has been authored by Peter Lindahl,under US Government Contract no. FA8650-08-D-2806. The U.S. Government hasunlimited rights to use, reproduce, and distribute this information.

ii

APPROVAL

of a thesis submitted by

Peter Allan Lindahl

This thesis has been read by each member of the thesis committee and has beenfound to be satisfactory regarding content, English usage, format, citations, biblio-graphic style, and consistency, and is ready for submission to the Division of GraduateEducation.

Dr. Steven R. Shaw

Approved for the Department of Electrical and Computer Engineering

Dr. Robert C. Maher

Approved for the Division of Graduate Education

Dr. Carl A. Fox

iii

STATEMENT OF PERMISSION TO USE

In presenting this thesis in partial fulfullment of the requirements for a master’s

degree at Montana State University, I agree that the Library shall make it available

to borrowers under rules of the Library.

If I have indicated my intention to copyright this thesis by including a copyright

notice page, copying is allowable only for scholarly purposes, consistent with “fair

use” as prescribed in the U.S. Copyright Law. Requests for permission for extended

quotation from or reproduction of this thesis in whole or in parts may be granted

only by the copyright holder.

Peter Allan Lindahl

April, 2009

iv

ACKNOWLEDGEMENTS

I would like to thank Dr. Steven Shaw for allowing me to take part in this

project and for his advice and support through out its duration. His willingness

to share his technical knowledge and professional experiences as well as answer

questions and concerns is greatly appreciated.

I would also like to thank: Eric Moog for his help in all facets of component

testing; particularly for his alacrity and precision in the modification of motor

controllers, Chris Colson for his general support and ideas, and the other faculty

and students at Montana State University who have helped me along the way.

Finally, I want to express my appreciation to my family and friends for their

unrelenting support through the ups and downs of graduate school.

Portions of this thesis were previously published and presented at the 2009

Institute of Electrical and Electronics Engineers (IEEE) Aerospace Conference

under the title, Simulation, Design and Validation of a UAV SOFC Propulsion

System, ©2009, Institute of Electrical and Electronics Engineers.

Funding Acknowledgment

Finally, I would also like to thank the United States Air Force Research Lab-

oratory and the National Science Foundation grant 0547616 for their respective

roles in supporting my research.

v

TABLE OF CONTENTS

1. INTRODUCTION ........................................................................................1

Current State of Fuel Cell Powered UAVs.......................................................1Steady-state Optimization Approach ..............................................................3Thesis Organization ......................................................................................4

2. SYSTEM MODEL ........................................................................................6

Solid Oxide Fuel Cell ....................................................................................7SOFC Emulation..................................................................................... 11

Brushless DC Motor System ........................................................................ 12BLDC Motor .......................................................................................... 12Motor Controller ..................................................................................... 15

Propeller .................................................................................................... 18

3. SIMULATION PROGRAM ......................................................................... 21

4. EXPERIMENTAL SETUP.......................................................................... 27

Instruments ................................................................................................ 29Fuel Cell Emulator Voltage and Current ................................................... 31Duty Cycle ............................................................................................. 31Motor Torque and Propeller Thrust.......................................................... 31Propeller Rotational Speed ...................................................................... 31Wind Tunnel Velocity and Air Density ..................................................... 32

Test Schedule.............................................................................................. 33Test Procedure ........................................................................................... 33

5. EXPERIMENTAL RESULTS...................................................................... 35

Fuel Cell Modeling Results .......................................................................... 35BLDC Motor Modeling Results.................................................................... 42Propeller Modeling Results .......................................................................... 52Measurement Uncertainty............................................................................ 58

6. CONCLUSION........................................................................................... 61

Future Work ............................................................................................... 61

REFERENCES CITED.................................................................................... 63

vi

TABLE OF CONTENTS – CONTINUED

APPENDICES ................................................................................................ 66

APPENDIX A: Simulation Results ............................................................ 67

APPENDIX B: Wind Tunnel Test Results ................................................. 93

vii

LIST OF TABLESTable Page

2.1 Solution Vector Elements .......................................................................7

2.2 Fuel Cell Models ................................................................................. 11

2.3 Motors................................................................................................ 15

2.4 Propellers ........................................................................................... 19

4.1 Propulsion System Test Schedule.......................................................... 34

5.1 Measurement Confidence Intervals ........................................................ 58

B.1 SOFC Model 08, AXI Double 5330/20 Motor, APC 22 x 12 Prop WindTunnel Data........................................................................................ 95

B.2 SOFC Model 08, AXI 5345/14 Motor, APC 27 x 13 Prop Wind TunnelData................................................................................................... 96




B.6 SOFC Model 09, AXI 5345/14 Motor, APC 26 x 15 Prop Wind TunnelData................................................................................................. 100

B.7 SOFC Model 09, AXI Double 5345/18 Motor, APC 22 x 12 Prop WindTunnel Data...................................................................................... 101





viii

LIST OF TABLES – CONTINUEDTable Page














ix

LIST OF FIGURESFigure Page

1.1 Fuel Cell Propulsion System Operation...................................................4

2.1 Fuel Cell Propulsion System Overview ....................................................6

2.2 Solid Oxide Fuel Cell .............................................................................9

2.3 SOFC Polarization Curve..................................................................... 10

2.4 Brushless DC (BLDC) motor system topology 2.4(a) and required con-troller operation 2.4(b) ........................................................................ 13

2.5 AXI 5345/14 BLDC Motor .................................................................. 15

2.6 Modified Jeti Spin99 Motor Controller.................................................. 17

2.7 APC 22 x 12 in. Propeller Coefficients of Power & Thrust ..................... 20

3.1 Simulation Program Output of Well Designed Propulsion System........... 22

3.2 Simulation Program Output of Poorly Designed Propulsion System........ 24

3.3 Simulation Program Output with Second Source ................................... 26

4.1 Wind Tunnel and Test Stand Setup...................................................... 28

4.2 Wind Tunnel Calibration ..................................................................... 30

4.3 Mock Fuselage..................................................................................... 32

5.1 Polarization Curve for SOFC PNNL Model 08 ...................................... 36






5.7 AXI DBL 5330/20 Voltage vs Speed ..................................................... 44

5.8 AXI DBL 5330/20 Torque vs Current ................................................... 45

5.9 AXI 5345/14 Voltage vs Speed ............................................................. 46

5.10 AXI 5345/14 Torque vs Current ........................................................... 47

x

LIST OF FIGURES – CONTINUEDFigure Page





5.15 APC 22 in. x 12 in. Propeller Measured Performance ............................ 54




A.1 SOFC Model 8, AXI 5330 DBL Motor Simulation Results ..................... 69

A.2 SOFC Model 8, AXI 5345-14 Motor Simulation Results ......................... 70


A.4 SOFC Model 8, AXI 5360 Motor Simulation Results ............................. 72

A.5 SOFC Model 9, AXI 5330 DBL Motor Simulation Results ..................... 73



A.8 SOFC Model 9, AXI 5360 Motor Simulation Results ............................. 76

A.9 SOFC Model 10, AXI 5330 DBL Motor Simulation Results.................... 77

A.10 SOFC Model 10, AXI 5345-14 Motor Simulation Results ....................... 78


A.12 SOFC Model 10, AXI 5360 Motor Simulation Results............................ 80






xi

LIST OF FIGURES – CONTINUEDFigure Page








xii

LIST OF SYMBOLS

Symbol Description Units

a Motor phase a -b Motor phase b -c Motor phase c -CP Propeller coefficient of power -CT Propeller coefficient of thrust -D Motor controller duty cycle -Ecell Ideal individual fuel cell voltage Ven motor phase n back emf VIc Current at fuel cell stack terminals AIcell Individual fuel cell currentIm Effective motor current Ain Motor phase n current AI0 Motor no-load current AJ Advance ratio -K Motor speed constant V s/radL Propeller diameter mLm Motor inductance per winding HNc Number of series connected fuel cells -np Propeller speed rev/sRm Motor resistance per winding ΩRth Thevenin equivalent approximated

fuel cell ohmic resistance ΩS Air craft speed / Measured wind tunnel velocity m/sT Propeller thrust NVc Voltage at fuel cell stack terminals VVcell Individual fuel cell voltage VVcell,act Individual fuel cell activation

voltage loss V

xiii

LIST OF SYMBOLS – CONTINUED

Symbol Description Units

Vcell,con Individual fuel cell concentrationvoltage loss V

Vcell,ohm Individual fuel cell ohmicvoltage loss V

Vm Effective motor voltage Vvn Motor phase n voltage VVoc Linear approximated open circuit

fuel cell stack voltage VV0 Motor no-load voltage V

Greek Symbolsαn Coefficients of quadratic approximation

of propeller coefficient of power CP -α′n Coefficients of quadratic approximation

of motor torque τ -β Motor drag coefficient N-m s/radρ Air density kg/m3

τ Motor torque rad/sτe Motor torque of electric origin rad/sω Motor speed N-m

xiv

ABSTRACT

This thesis presents a physically-based model for design and optimization of afuel cell powered electric propulsion system for an Unmanned Aerial Vehicle (UAV).Components of the system include a Solid Oxide Fuel Cell (SOFC) providing power,motor controller, Brushless DC (BLDC) motor, and a propeller. Steady-state modelsfor these components are integrated into a simulation program and solved numerically.This allows an operator to select constraints and explore design trade-offs betweencomponents, including fuel cell, controller, motor and propeller options. We alsopresents a graphical procedure using the model that allows rapid assessment andselection of design choices, including fuel cell characteristics and hybridization withmultiple sources. To validate this simulation program, a series of experiments con-ducted on an instrumented propulsion system in a low-speed wind tunnel is providedfor comparison. These experimental results are consistent with model predictions.

1

INTRODUCTION

In recent years, fuel cells have received increased interest for their ability to effect

efficient, quiet, and clean conversion of chemical to electrical energy. These attributes

also make fuel cells an attractive power source for electric propulsion and a possible

alternative to gasoline powered internal combustion (IC) engines in Unmanned Aerial

Vehicles (UAVs). Potential advantages of fuel cell / electric UAV propulsion include

decreased emissions, increased efficiency, increased range and loiter time, and quieter,

lower profile flight. Additionally, because fuel cells are chemical to electrical energy

conversion devices, while IC engines are chemical to mechanical, an added advantage

is the readily available electricity for UAV payloads such as surveillance equipment.

Current State of Fuel Cell Powered UAVs

To date, several fuel cell powered UAVs have been built and successfully flown

[1, 2, 3]. However, documented design and optimization processes have been limited.

In 2004, Ofoma and Wu [4] presented a design methodology for developing a fuel cell

powered UAV used as a remote sensing tool, finding that fuel cell selection was a

major driver in aircraft design. While this study investigated many important facets

of propulsion system and aircraft design, the study was not integrated and often

only qualitative in nature. The study did compare simulated propeller thrust values

and air foil lift values generated with the web-based software code, Javaprop and

Javafoil to experimental results, but the thrust experiments utilized batteries which

have significantly different current/voltage characteristics from fuel cells. Further,

the criteria used for fuel cell selection was limited to power ratings, weight and cost

2

with no investigation into the current and voltage coupling requirements between the

fuel cell and motor.

In 2005, Soban and Upton [5] described a completely integrated qualitative map-

ping scheme designed to narrow the classes of UAVs best suited for fuel cell propulsion.

In this study, propulsion architectures were broken down into classes of components,

i.e. fuel cell type, fuel type, and fuel storage systems, and their associated measures

of effectiveness such as fuel consumption rates, emissions, and power density. Aircraft

architecture was split into classes of UAVs represented by current UAV systems such

as Pioneer and Predator, with each class assigned common vehicle performance ratings

for performance requirements such as range, altitude, and rate of climb. Through a

combination of several commonly used qualitative assessment tools, optimal propul-

sion designs were assigned to different UAV classes. The findings of the study sug-

gested that while current fuel cell technology was inferior to conventional propulsion

systems, the anticipated advances in fuel cell technology, particularly that of solid

oxide fuel cells (SOFCs), hold significant advantages in UAVs designed for long range

and long endurance flights.

Between 2005 and 2007, members of the Aerospace Systems Design Laboratory at

the Georgia Institute of Technology designed and built a proton exchange membrane

(PEM) fuel cell demonstration UAV [1, 6, 7]. In [6], the authors describe the two

level approach used in design and construction of the aircraft. The top level of this

approach is a conceptual task used to explore the design space for optimal UAV

designs. The design space is comprised of five contributing analyses (CAs): aero-

dynamic simulation, propulsion system analysis, weights tabulation and calculation,

performance analysis and hydrogen storage. These CAs are assembled into a design

structure matrix allowing assessment of millions of combinations of UAV designs and

components. The optimal conceptual design is selected based on thrust margin, the

3

thrust available divided by thrust required for a given air speed, and overall propulsion

efficiency. Using this conceptual design, the low level task provides a more in depth

analysis focusing on design and integration of the fuel cell system and improvements

upon the aerodynamic design of the aircraft. From this study, a demonstrator fuel

cell UAV was constructed utilizing a 32 cell, 500 W PEM fuel cell power plant [7].

The results of this project suggest that the proper matching of motor and propeller

to the characteristics of a given fuel cell is the most important aspect of a successful

design.

While these studies point to fuel cell technology as a promising alternative to

conventional IC engine propulsion systems, they also emphasize the importance of fuel

cell selection and propulsion system component matching to fuel cell characteristics in

the design of the aircraft. This thesis presents a steady-state optimization approach

and a graphical procedure for investigating the performance implications of various

propulsion system components and fuel cell models.

Steady-state Optimization Approach

For long endurance UAVs, the aircraft spends the majority of its flight time in

steady flight mode, i.e. constant velocity. Thus, the propulsion system should be

optimized at its required operation point for steady flight. Figure 1.1 shows fuel cell

data for a typical flight test of the Georgia Institute of Technology demonstrator UAV

described in [6, 7].

The figure shows three regions of operation. Region one is idle operation with

the propeller static. The low level current draw seen here is the result of powering

auxiliary equipment and the balance of plant of the fuel cell. Region two starts

around the 6 second mark and is the high powered condition corresponding to take

4

Figure 1.1: Sample data for a straight line flight test of the 500 W Proton ExchangeMembrane (PEM) fuel cell powered demonstrator UAV detailed in [7]. Figure usedwith permission of author. ©American Institute of Aeronautics and Astronautics.

off and climbing. Around the 48 second mark, region three begins. Current draw is

reduced and the aircraft assumes steady flight for about 8 seconds before descending

and landing. The steady flight region is very short in this test flight. However, for

a long endurance UAV deployed in a real world application, this is the region of

primary operation. This is the region of propulsion system operation that should be

optimized. It should be noted however that final propulsion system design must be

able to provide adequate power for all three regions of operation. From Figure 1.1

we see that for UAV steady flight, the operation of the propulsion system remains

relatively constant and thus can be accurately described using steady-state models of

its components.

Thesis Organization

This thesis considers the steady-state modeling, design, and component selection

for a fuel cell powered electric propulsion system. Chapter two discusses in depth

5

the major components of the propulsion system along with first-order mathematical

models used to describe their operation. In addition, information is provided for

the corresponding components used in the experimental validation part of the thesis.

In chapter three, the simulation program comprised of these models is explained,

and a graphical solution approach that allows easy assessment of design choices, e.g.

changing stack specifications, is presented. Chapters four and five describe the wind

tunnel testing procedure aimed at verifying the individual component models and the

results of the tests, respectively. The thesis concludes in chapter six with discussion

of the project’s successes, necessary improvements, and recommendations for further

work.

6

SYSTEM MODEL

Figure 2.1 depicts the propulsion system investigated in this thesis. The system is

comprised of an SOFC fuel cell providing electrical power to a Brushless DC (BLDC)

motor system that converts the electricity to mechanical power for turning a propeller.

The input to the system is the duty cycle, D, which controls the voltage and current

applied to the motor, while the output is the thrust, T produced by the propeller. Of

particular concern is the optimization of power delivery from the fuel cell terminals

to the propeller.

Figure 2.1: The propulsion system considered is comprised of four major components:the SOFC fuel cell stack, the BLDC motor and controller and the propeller. The inputto the system is the duty cycle, D and the output is thrust, T [8], ©2009, Instituteof Electrical and Electronics Engineers.

The primary purpose of the simulation program, described in further detail in

chapter three, is to explore the performance implications of different fuel cell per-

formance characteristics, operating points, and component choices for motor and

propeller in the block diagram in Figure 2.1. To accommodate various component

models, explicit modularity is maintained in the program codes which is mirrored

in the descriptions of components in the following paragraphs. These models are

7

numerically combined to find an overall solution vector(Ic Vc D Im Vm ω τ T

)(2.1)

the components of which are detailed in the descriptions of each subsystem, below.

The elements of this solution vector can be constrained in the simulation, and the

program solved to find the non-constrained elements. Table 2.1 defines these elements.

Table 2.1: Elements contained in the solution vector of equation 2.1

Symbol Quantity UnitsIc Current at fuel cell terminals AVc Voltage at fuel cell terminals VD Motor controller duty cycle -Im Effective motor current AVm Effective motor voltage Vω Motor speed rad/sτ Motor torque N-mT Propeller thrust N

The following sections describe the operation of the individual components of the

propulsion system in Figure 2.1, their first-order steady-state mathematical models,

and the corresponding physical components used in the test stand.

Solid Oxide Fuel Cell

Fuel cells are electrochemical devices that convert chemical energy, stored in

hydro-carbon fuel, into electrical energy. The basic structure of a fuel cell consists of

three layers: the anode (negative electrode), the cathode (positive electrode), and a

thin electrolyte layer separating the two. Fuel is supplied to the anode while an oxi-

dant is fed to the cathode. The electrochemical reaction occurring at the boundaries

8

between the electrodes and the electrolyte produces an electric current through the

electrolyte that is returned through a complimentary external load [9].

Fuel cell types are typically distinguished by their electrolyte technology, which

dictates the type of ionic conduction through the electrolyte [9, 10, 11]. For example,

PEM fuel cells employ a proton conducting polymeric ion exchange membrane, while

the electrolyte in an alkaline fuel cell (AFC) is an hydroxide ion (OH−) conducting

aqueous alkaline solution. SOFCs have a solid metal oxide electrolyte and operate at

high temperatures, usually between 600 C and 1000 C, where the ionic conduction

of oxygen ions (O2−) occur. The high temperature operation and ionic conduction

of oxygen in SOFCs hold several advantages over other fuel cells. Most notably for

military applications, this combination allows the possibility for internal reformation

of heavy hydrocarbon fuels such as JP-8 jet fuel and diesel fuel. Additionally, SOFCs

are potentially less susceptible than other fuel cell technologies to poisoning from low

level sulfur content in hydrocarbon fuels, and carbon-monoxide (CO), a potential

byproduct of fuel reformation and poisonous to PEM fuel cells, acts as a fuel in

SOFCs [9, 10].

Figure 2.2 shows conceptual and actual images of an SOFC. Oxygen acquires

electrons from the external circuit in the porous, electrically conductive cathode. The

resulting oxygen ions diffuse readily toward the reducing atmosphere at the anode by

means of oxygen vacancies in the lattice of the electrolyte. The electrolyte has a

low electronic conductivity. Oxygen ions arriving at the anode combine readily with

reformed fuel constituents, (H2 and CO), and give up electrons to the external circuit.

The result of this energetically favorable process is direct conversion of chemical to

electrical energy, without the efficiency implications of a heat engine.

The Scanning Electron Micrograph (SEM) image in Figure 2.2(b) of an anode

supported cell provides some indication of the actual scale of a fuel cell structure.

9

(a) Solid Oxide Fuel Cell Diagram (b) SEM Image of SOFC

Figure 2.2: (a) Cross-sectional conceptual diagram and (b) scanning electron micro-graph of a solid oxide fuel cell [8], ©2009, Institute of Electrical and ElectronicsEngineers.

The anode appears on the left of the SEM image. The thickness of the anode provides

structural support. The electrolyte and cathode appear on the right margin above

the scale bar.

Fig. 2.3 shows measured data representing the current voltage relationship of a

typical anode supported fuel cell. The data in Fig. 2.3 is for an InDEC anode-

supported cell with an active area of 18 cm2, at 750 C, operating on oxygen and

hydrogen. The output voltage of an SOFC can be characterized as

Vcell = Ecell − Vcell,act − Vcell,ohm − Vcell,con (2.2)

Ecell, represents the ideal performance of the fuel cell and is dependent on the operat-

ing temperature of the cell and the reactants involved. Vcell,act, Vcell,ohm, and Vcell,con

are voltage losses due to an electrochemical activation process, ohmic resistances in

the cell components, and finite mass transport rates, respectively [9, 12]. In equation

2.2, contributions of the anode and cathode are lumped. These losses dominate dif-

10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Current Density (A/cm2)

Fue

l Cel

l Vol

tage

(V

) ActivationRegion

Ohmic Region ConcentrationRegion

Figure 2.3: Measured current-voltage relationship of a typical InDEC anode sup-ported SOFC [8], ©2009, Institute of Electrical and Electronics Engineers.

ferent regions of the polarization curve as depicted in Figure 2.3. Individual cells are

typically “stacked”, or connected in series, to form a power source with convenient

output voltages. Fuel cell stack operation is derived from the individual cell operation

by

Vc = NcVcell (2.3)

where Nc is the number of series connected cells [12]. In the UAV application, it is

reasonable to assume that the stack will be designed under a weight constraint so

that the nominal operating point is near the peak power point in the ohmic region

of the fuel cell curve. In the ohmic region, the fuel cell can be approximated by a

Thevenin circuit equivalent, i.e.

Vc = Voc − IcRth, (2.4)

where Voc is the zero-current voltage intercept of the linear approximation of the

ohmic part of the response, and Rth is the slope.

11

Table 2.2 lists the characteristics for the six fuel stacks involved in this study.

Research and design of the fuel cell stacks took place at the Pacific Northwest National

Laboratory (PNNL) in Richland, Washington. The specified operating voltages, Vc

correspond to optimal voltage levels for producing around 2 kW of electric power as

dictated by PNNL.

Table 2.2: Physical and modeling parameters of the SOFC stacks investigated

Fuel Cell Nc Vcell (V) Voc (V) Rth (Ω) Vc (V)Model 8 67 0.7 70.1 0.55 46.9Model 9 60 0.7 67.3 0.55 42Model 10 60 0.625 66.4 0.55 37.6Model 11 67 0.625 67.8 0.55 41.9Model 12 73 0.625 57.8 0.28 45.6Model 13 73 0.7 62.0 0.28 51.1

SOFC Emulation

Because operating a multi-kW SOFC stack is expensive and requires significant

infrastructure, an SOFC emulator was built to mimic steady-state stack operation for

testing purposes. A 10 kW Sorenson DCR 160-62T power supply in combination with

a resistor built from a variable-length of 6.4 mm diameter 316 stainless steel tube was

used to recreate fuel cell Ohmic Region polarization characteristics at power levels in

the laboratory. A Miller Coolmate 4 welding torch cooling system rated for 4.4 kW

was used to stabilize the temperature (and therefore the resistance) of the stainless

steel by circulating a low-conductivity coolant through the tubing.

12

Brushless DC Motor System

Brushless DC (BLDC) motors feature high efficiency, ease of control, and aston-

ishingly high power density at reasonable shaft speeds [13]. In general, BLDC motors

outperform conventional permanent DC motors with better speed and torque char-

acteristics, efficiency, longer operating lives, and increased reliability [14, 15]. These

features make BLDC motors a natural choice for electric propulsion of small craft.

BLDC motors are permanent magnet synchronous motors, which from a modeling

standpoint are similar to conventional permanent magnet DC motors [16]. The salient

difference is that the BLDC motor is commutated externally by power electronic

switches rather than by the brushes and commutator built into a standard DC motor.

This introduces some electronic complexity, as an external controller is required to

switch three phases of windings according to a real-time estimate of the rotor position.

Figure 2.4(a) shows the topology of a typical sensorless three-phase BLDC motor

system. The inverter used in the motor controller is the same as a conventional three-

phase inverter, however because the permanent magnet motor used has trapezoidal

shaped back emfs, rectangular stator currents are required to produce constant torque

[13, 17]. This operation is illustrated in Figure 2.4(b).

BLDC Motor

For steady-state modeling purposes, the modeling complexity of the BLDC con-

troller is ignored so that the motor and controller is treated “as commutated”, i.e. the

controller estimates the rotor position and commutates the motor efficiently in the

steady-state. Under this assumption, the system can now be treated as an ideal DC

machine with current Im, voltage Vm, and resistance 2Rm. The equations describing

13

(a) BLDC Motor Topology

ia

ea

π/6 5π/67π/6

ib

eb

π/25π/6 3π/2

ic

ec

π/6π/2 7π/6

(b) BLDC Drive Signals and Back Emf Relationship

Figure 2.4: Brushless DC (BLDC) motor system topology 2.4(a) and required con-troller operation 2.4(b)

14

the motor are then

Vm = Kω + 2RmIm (2.5)

τe = KIm, (2.6)

where K is the motor speed constant, ω is the shaft speed, τe is the torque of electric

origin, and Rm is the winding resistance. Values for K and Rm are typically supplied

by the manufacturer. Note that Rm appears with a factor of two in this equation

because resistance is specified per winding and two windings are in series for each

commutating sequence.

Motor manufacturers also typically provide current I0 and voltage V0 data under

“no-load” conditions to indicate the amount of core, friction and windage losses during

steady-state motor operation [9]. These losses are lumped together as a windage loss

by calculating a drag coefficient

β =K2I0

V0 − 2I0Rm

, (2.7)

which modifies the output torque τ to ensure that the motor model passes through

the specified no-load operating point, i.e.

τ = τe − βω. (2.8)

The net mechanical output is torque τ at speed ω.

Several motors made by AXI Model Motors were selected for evaluation in the

test stand. These motors advertise efficiencies in excess of 90% at the power levels

required and have speed constants in a range which does not require a gear box

between motor and propeller. Parameters for the motors are listed in Table 2.3. The

values for I0 correspond to V0 = 30V. For an indication of motor size, the first two

numbers in the motor name give the rotor diameter (mm), and the second two give

15

Table 2.3: Modeling parameters of the AXI motors investigated [8], ©2009, Instituteof Electrical and Electronics Engineers.

Motor K (Vs rad−1) Rm (Ω) I0 (A)AXI Double 5330/20 0.041 0.012 4.8AXI 5345/14 0.042 0.014 2.6AXI 5345/18 0.056 0.021 1.6AXI 5360/20 0.080 0.034 1.8

Figure 2.5: AXI 5345/14 BLDC Motor

the stator length (mm). The AXI 5345/14 motor is shown in Figure 2.5. The AXI

Double 5330/20 motor is two 5330/20 motors sharing a common rotor.

Motor Controller

In addition to switching the output transistors with rotor position, which is

lumped with the model motor, the motor controller can introduce a duty cycle D

in the pulses applied to the motor windings. The duty cycle is the input to the

propulsion system allowing flight control to change power delivered to the prop. From

the power electronics perspective, the average motor voltage over a commutating se-

16

quence is modulated by D, so the duty cycle effectively introduces an integrated buck

converter. Assuming the converter is lossless, the equivalent voltage Vm and current

Im at the motor terminals are given by

Vm = DVc (2.9)

Im =1

DIc, (2.10)

where D is the duty cycle and Vc, Ic are the fuel cell voltage and current. Losses in

the motor controller are neglected because they are estimated to be on the order of

10 W while the motor is drawing in excess of 1 kW.

For all laboratory tests, Jeti Spin99 motor controllers were used. These controllers

are designed for the appropriate power levels, but are intended for use with NiMH

or Li based batteries that have low series resistance compared to the fuel cell. As

a result, the no-load voltages in the fuel cell systems exceed the voltage rating of

the parts used in these controllers. The Spin99 controllers were disassembled and

the power MOSFETS and capacitors were replaced with higher voltage rated parts.

Figure 2.6 depicts the process. An Agilent 33220A function generator replaced the

radio controlled transmitter and receiver associated with the motor controller allowing

precise control of duty cycle.

17

(a) Disassembled Motor Controller

(b) Modified Motor Controller

Figure 2.6: Components of the Jeti Spin99 motor controller were replaced with compo-nents that matched the voltage requirements of the fuel cell systems studied. 2.6(a)shows the completely disassembled controller, and 2.6(b) shows the modified con-troller

18

Propeller

The propeller determines the relationship between motor speed and load torque,

and therefore ultimately determines the operating point of the propulsion system.

Typically, propeller performance is expressed using dimensionless thrust coefficient

CT and power coefficient CP . The coefficients are functions of the relative speed of

the craft and the prop, or the advance ratio

J =S

npL, (2.11)

where S is the air speed, np = ω2π

is the rotational speed of the prop in revolutions

per second, and L is the prop diameter [18]. Given CP at a particular advance ratio,

the shaft power required is

P = CPρL5n3

p, (2.12)

where ρ is the local air density. Setting the propeller power requirement equal to the

mechanical power at the shaft, i.e. τω = P , yields the desired relationship between

motor speed and torque

τ = CPρL5 ω2

(2π)3(2.13)

Similarly, given CT , the thrust produced by the propeller is

T = CTρL4n2

p (2.14)

For steady flight, the thrust and lift produced by the propulsion system and wings,

respectively, must be sufficient to overcome the aircraft’s drag and weight. The

relationship between these forces acting on an aircraft and the craft’s air speed is

complex, and requires an understanding of the aerodynamic properties of the vehicle

and the flight profile. The simulation program simply calculates the available thrust

19

Table 2.4: APC brand propellers used in wind tunnel testing and the 2nd order modelsused to describe their operation [8], ©2009, Institute of Electrical and ElectronicsEngineers

Propeller CoefficientsAPC 22x12 CT = −0.039J2 − 0.055J + 0.062

CP = −0.049J2 − 0.001J + 0.031APC 24x12 CT = −0.038J2 − 0.055J + 0.057

CP = −0.045J2 − 0.005J + 0.028APC 26x15 CT = −0.040J2 − 0.053J + 0.067

CP = −0.053J2 − 0.002J + 0.042APC 27x13 CT = −0.037J2 − 0.055J + 0.054

CP = −0.044J2 − 0.005J + 0.026

at a target airspeed. If this number is in excess of the thrust requirement anticipated

by the airframe designer, the craft is predicted to fly.

Four lightweight APC composite propellers were selected for testing in the wind

tunnel. For each propeller, APC provided estimated values of CP and CT for discrete

values of J . Figure 2.7 shows an example of these relationships along with second

order polynomial trendlines fit to the data using the least-squares method. These

polynomials capture CT and CP as continuous functions of J for use in the simulation

program. Table 2.4 show these functions for the four propellers selected. The first

number in the propeller specification is the diameter in inches, while the second

number is the pitch in inches. The pitch of a propeller defines the distance the

propeller would travel in one revolution if there were no slip.

20

(a) Coefficient of Power

(b) Coefficient of Thrust

Figure 2.7: Power and Thrust coefficient plots for the APC 22 x 12 in. propeller.

21

SIMULATION PROGRAM

The simulation program is comprised of four analysis functions corresponding to

the mathematical models presented in chapter two. Parameters of the individual

component models (Tables 2.2, 2.3 and 2.4) are stored in global variables and serve

as inputs to the analysis functions. With a user-specified controller duty cycle, D,

aircraft flight speed, S and local air density, ρ, the combined analysis functions can

be solved with standard techniques to find the system operation point, defined in

equation 2.1. While this solution is valuable information, it does not provide design

insight needed to understand trade-offs in fuel cell output characteristics, control

opportunities, or the relative merit of different propeller and motor combinations.

Rather than solving for a single operating point found from a single input variable, it

is more useful to solve for a collection of operating points that can be presented in a

graphical format. The most intuitive independent variable for this purpose appears to

be the fuel cell stack terminal current Ic. Numerically, Ic is constrained to a succession

of values from a vector, and the matlab command fsolve() is used to determine every

other variable as a function of current. The outputs are then reflected to the fuel cell

terminals where they can be interpreted on one plot in conjunction with the fuel cell

response.

Figure 3.1 shows a sample output. This two dimensional voltage/current space

represents the design space of the fuel cell stack. The line labeled “linearized FC

curve” is simply a plot of the output characteristic of one specific fuel cell stack. In

this example, SOFC PNNL Model 12 with an open circuit voltage of 57.8 V and a

Thevenin equivalent resistance of 0.28 Ω is used. The red box, labeled “propeller and

motor operation region”, represents a family of voltage/current curves for the motor

and propeller combination at the specified airspeed. The lower margin of this box

22

10 20 30 40 50 60 70 800

20

40

60

80

100

Current at fuel cell terminals (A)

Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.5 N

20 N

35 N

50 N

D = 0.5

D = 1

Lines ofConstant Thrust

Linearized FC Curve

Propeller and Motor Operation Region

Figure 3.1: Predicted performance of the PNNL Model 12 SOFC, AXI 5345/18 motor,Jeti Spin 99 controller and APC 27x13 in. propeller. The simulation was performedassuming a cruising velocity of 31.3 m/s (70 mph) and air density of 1.2 kg/m3.

23

shows the relationship between current and voltage for the motor and propeller with

duty cycle D = 1. The upper margin of the box is the curve corresponding to D = 0.5.

The operating point of the propulsion system is determined by the intersection of the

motor/propeller curve at a specified duty ratio and the fuel cell curve. Thus, the

interpretation of the graph is that any point on the fuel cell curve within the box

is an achievable operating point at a reasonable steady-state duty ratio between 0.5

and 1.

The other variables of equation 2.1 can also be constrained to provide interpre-

tation of the achievable operating points. Contours of constant thrust are added

to the plot by constraining thrust, T , to specific values and repeating the solution

process. These are the dashed lines labeled with thrust values. These curves provide

current/voltage relationships required for the motor and propeller to produce the

thrusts specified.

The operating point as specified by the PNNL defined optimal fuel cell output

voltage is found by constraining Vc to the Vop value of 45.6 V. This is indicated by a

large point in Figure 3.1 and shows the estimated thrust to be 39.5 N at a duty ratio

of roughly 0.75. With relatively high estimated thrust and an operation point well

within the duty cycle limits of the propeller and motor operation region, Figure 3.1

represents a good propulsion system design.

In contrast, Figure 3.2 shows a poor combination of components, the AXI 5360/20

motor and APC 22 x 12 propeller, for the same fuel cell parameters. In this case,

it is not possible to select a duty ratio where the motor and propeller are even able

to use the power that the fuel cell is capable of delivering. The nominal fuel cell

operating point is outside of the propeller curve box, demonstrating that this system

is also incapable of producing the thrust achieved by the system in Figure 3.1. At

the maximum duty ratio of 1.0, this system would only produce slightly more than

24

10 20 30 40 50 60 700

20

40

60

80

100

120

140

160

180

200


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

37.1 N

20 N

35 N

50 N

D = 0.5

D = 1


Linearized FC Curve

Propeller and MotorOperation Region

Figure 3.2: Predicted performance of the PNNL Model 12 SOFC, AXI 5360 motor,Jeti Spin 99 controller and APC 22x12 in. propeller. The simulation was performedassuming a cruising velocity of 31.3 m/s (70 mph) and air density of 1.2 kg/m3.

25

20 N of thrust. Furthermore, even if it were possible to command the necessary duty

cycle, Figure 3.2 is predicted to produce less thrust at the same power level.

Graphs of these kind immediately connect the quantities of interest to the fuel

cell stack designer, i.e. current and voltage at the stack terminals, to the ability

to command thrust, which is of interest to the airframe designer. Additionally, the

graphs lend themselves to understanding how the current/voltage characteristics of

a fuel cell might be modified with an auxiliary source, e.g. photovoltaics or bat-

tery, and the effect that the new current/voltage characteristic might have on flight

performance. As a specific example, the inherently sloping fuel cell curves tend to

become parallel to lines of constant thrust at higher currents. Even if the fuel cell is

subjected to severe high-current loading, very little additional thrust is possible. On

the other hand, an alternate source with a flat current voltage characteristic could be

used to temporarily cross several thrust curves and substantially increase the flight

envelope. This idea is illustrated in Figure 3.3 with the dotted line indicating the

polarization curve of an second power source with a flat current voltage relationship.

The 3 kW operating point shown would still draw only 2 kW from the fuel cell with

the remaining 1 kW of power being provided by the secondary source.

Appendix A contains the full set of simulation results for all combinations of

propulsion system components.

26

10 20 30 40 50 60 70 800

20

40

60

80

100


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.5 N3 kW

56.8 N

20 N

35 N

50 N

D = 0.5

D = 1


Linearized FC Curve

Propeller and Motor Operation Region

Figure 3.3: Predicted performance of the propulsion system of Figure 3.1 with anadded second power source. The simulation was performed assuming a cruising ve-locity of 31.3 m/s (70 mph) and air density of 1.2 kg/m3.

27

EXPERIMENTAL SETUP

As indicated in chapter two, the propeller models relate thrust, T , and torque,

τ , to the advance ratio, J (equations 2.11, 2.13 and 2.14). These models assume a

non-zero free-stream velocity, S, up stream of the propeller. Thus, static propeller

tests are inadequate for verifying propeller models. An open circuit wind tunnel,

Figure 4.1(a), was constructed for the purpose of testing propulsion systems under

flight conditions. The working section of the wind tunnel is 91 cm x 91 cm and 3 m in

length. Ideally, the wind tunnel would be capable of an air flow velocity equivalent to

the 30 m/s desired aircraft velocity. However, this would require a significantly large

and expensive excitation fan that would exceed our available lab space and budget.

Instead, the wind tunnel is excited by a 3.7kW, 91cm diameter Dayton tube-axial duct

fan upstream of the propeller capable of wind tunnel velocities around 40% aircraft

velocities. Data achieved at these lower wind tunnel velocities can be extrapolated

to predict performance at actual flight speeds.

A test stand was mounted in the working section of the wind tunnel 4.1(b). The

test stand consists of an interchangeable motor mounting plate fixed to a steel rod.

The rod is supported at its center of gravity on a pillow block, so that it is free to

translate and rotate. The rod is constrained by only a torque/force load cell which

provides direct measurement of motor torque and developed thrust. In addition to

torque and thrust, we measure atmospheric conditions, air speed, propeller speed, fuel

cell current and voltage, and duty cycle on the controller. This allows a comparison

of simulation variables with lab measurements. The propeller is mounted in a pusher

configuration.

As recommended in [19], both a screen and a honeycomb section were installed

in an effort to normalize the air flow through the wind tunnel. Screens have the

28

(a) Wind Tunnel

(b) Test Stand

Figure 4.1: The open circuit wind tunnel 4.1(a) and test stand 4.1(b) constructedfor testing propulsion system components [8], ©2009, Institute of Electrical andElectronics Engineers.

29

benefit of creating a more uniform flow velocity through the wind tunnel as well

as reducing turbulence intensity. Honeycombs reduce swirl and also have a minor

turbulence reduction effect. The screen was made of heavy duty nylon construction.

The honeycomb was constructed of 396 pieces of 1.5 inch PVC pipe 6 inch in length,

18 pieces to a row and 22 rows. To measure the effectiveness of these components, the

test stand was removed from the wind tunnel and a grid was constructed from kite

string along the cross section of the tunnel corresponding to the propeller location.

The grid consisted of 25 measurement locations as indicated by Figure 4.2. Velocity

measurements were taken using a Kestrel 3500 Weather Meter at each location with

the screen installed, the honeycomb installed and with neither installed. The instal-

lation point for both the screen and the honeycomb was 3 feet downstream of the

axial fan and 5 feet upstream of the propeller location.

With no normalizing device installed, the wind tunnel had an average wind speed

of 13.7 m/s and a maximum deviation from the average of 29%. Unexpectedly,

both screen and honeycomb had adverse affects on air flow. The screen caused a

reduction in average velocity to 9.7 m/s, and an increase in flow variation to 61%.

The honeycomb reduced the average velocity to 12.2 m/s and increased the maximum

variation in velocity to 43% from the average. Thus, it was determined that wind

tunnel testing should procede without either component installed. The effects of the

screen and the honeycomb on wind tunnel swirl were not measured.

Instruments

The instruments used to measure system operation for comparison with simulated

variables are described below.

30

(a) Honeycomb (b) Screen

(c) Nothing

Figure 4.2: Both a honeycomb and a screen were installed in the wind tunnel in anattempt to normalize air flow. The velocities measured are shown in m/s.

31

Fuel Cell Emulator Voltage and Current

As described in chapter two, a Sorenson DCR 160-62T in series with a stainless

steel resistor was used to simulate the steady-state performance of the fuel cell stacks.

The current delivered from the power supply, Ic was recorded off the power supply

ammeter which has an accuracy of 0.1%. Voltage at the emulated fuel cell terminals,

Vc was measured using a B&K Test Bench 389A digital multimeter. The 389A has

an accuracy of 0.25% for DC voltage readings.

Duty Cycle

Duty cycle D was recorded using a Tektronix P5205 high voltage probe in conjunc-

tion with a DPO 4054 Tektronix Oscilloscope. The P5205 has a maximum voltage

rating of 1300 V and bandwidth of 100 MHz.

Motor Torque and Propeller Thrust

Propeller torque τ and thrust T were measured using a Cooper LXT-920 force /

torque load transducer. The linearity, hysteresis and repeatability ratings for thrust

are ±1.8 N, ±0.9 N and ±0.4 N, respectively. These ratings for torque are ±0.045

N-m, ±0.023 N-m and ±0.011 N-m.

Propeller Rotational Speed

A CheckLine DT-205L non-contact tachometer was used to access the propeller’s

rotational speed ω. The DT-205L has a maximum measurement rating of 10,470

rad/s and an accuracy of 0.1 rad/s for the range of speeds observed.

32

Wind Tunnel Velocity and Air Density

The simulated craft velocity S and the atmospheric conditions used to calculate

air density ρ were measured using a Kestrel 3500 Weather Meter. For velocity, the

Kestrel has an operating range of 0.4 to 60 m/s, and 3% accuracy. Atmospheric

pressure, temperature and dew point are required for estimating air density. The

Kestrel’s accuracy for these measurements are ±1.5 hPa (hectopascals), ±1 C and

±2 C respectively.

Figure 4.3: A mock fuselage, 6 in. x 6.5 in. and 3 feet in length was constructedfor installation on the test stand. This allowed testing of propeller performance withpartial occlusion by the aircraft fuselage.

33

Test Schedule

With six fuel cell models, four BLDC motors and four propellers considered, a

complete study would involve 96 combinations of components. Additionally, a mock

aircraft fuselage was constructed for installation on the test stand (figure 4.3). With

the mock fuselage installed, tests could be repeated to determine if the UAV fuse-

lage would occlude the propeller enough to invalidate the propeller models used in

the simulation. To limit the number of tests required, an experiment schedule was

constructed so that each motor/propeller combination was tested at least once, and

that each fuel cell model was tested with each motor and each propeller at least once.

This allowed a comprehensive study of the possible components while reducing the

required testing to 25% of the total combinations. This schedule is displayed in Table

4.1. The results of these experiments are discussed in the next chapter, and presented

in full in Appendix B.

Test Procedure

Each experiment consists of two runs through the test procedure; the first with the

mock fuselage installed and the second without. First, the resistor is calibrated to the

desired fuel cell output resistance using a precise meter. The resistor cooling system

and wind tunnel excitation fan are then turned on. Atmospheric conditions and any

instrumentation offsets are then recorded. The power supply simulating the fuel cell

is then adjusted to the required open circuit Thevenin equivalent voltage. Then the

duty cycle command is adjusted until the desired operating point is achieved. All

variables are recorded, and the process is repeated for several duty cycle controlled

operating points.

34

Table 4.1: 24 of the 96 possible combinations of components were tested in the windtunnel. Each motor/propeller combination was tested at least once and each fuel cellmodel was tested with each motor and each propeller at least once. Results of thesetests are described in chapter five and listed in Appendix B.

Test FC Model Motor PropTest 1 PNNL Model 08 AXI DBL 5330/20 APC 22 x 12Test 2 PNNL Model 08 AXI 5345/14 APC 27 x 13Test 3 PNNL Model 08 AXI 5345/18 APC 24 x 12Test 4 PNNL Model 08 AXI 5360/20 APC 26 x 15Test 5 PNNL Model 09 AXI DBL 5330/20 APC 27 x 13Test 6 PNNL Model 09 AXI5345/14 APC 26 x 15Test 7 PNNL Model 09 AXI5345/18 APC 22 x 12Test 8 PNNL Model 09 AXI5360/20 APC 24 x 12Test 9 PNNL Model 10 AXI DBL 5330/20 APC 22 x 12Test 10 PNNL Model 10 AXI5345/14 APC 27 x 13Test 11 PNNL Model 10 AXI5345/18 APC 24 x 12Test 12 PNNL Model 10 AXI5360/20 APC 26 x 15Test 13 PNNL Model 11 AXI DBL 5330/20 APC 24 x 12Test 14 PNNL Model 11 AXI5345/14 APC 22 x 12Test 15 PNNL Model 11 AXI5345/18 APC 26 x 15Test 16 PNNL Model 11 AXI5360/20 APC 27 x 13Test 17 PNNL Model 12 AXI DBL 5330/20 APC 26 x 15Test 18 PNNL Model 12 AXI5345/14 APC 24 x 12Test 19 PNNL Model 12 AXI5345/18 APC 27 x 13Test 20 PNNL Model 12 AXI5360/20 APC 22 x 12Test 21 PNNL Model 13 AXI DBL 5330/20 APC 27 x 13Test 22 PNNL Model 13 AXI5345/14 APC 26 x 15Test 23 PNNL Model 13 AXI5345/18 APC 22 x 12Test 24 PNNL Model 13 AXI5360/20 APC 24 x 12

35

EXPERIMENTAL RESULTS

As outlined in chapter four, each test listed in Table 4.1 was conducted twice;

once with the mock fuselage installed and once without. These combinations of

components were assembled on the test stand in our wind tunnel and tested at a

variety of operating points. Using these operating points as inputs along with the

measured air density and wind tunnel velocity, the simulation program was run to

solve for individual component models.

Fuel Cell Modeling Results

Figures 5.1 - 5.6 show the experimental results for the six fuel cell models. Each

fuel cell model was tested with four different motor/propeller loads which are indi-

cated in the accompanying figure legend. The blue line in each figure is the simulated

ohmic region of the fuel cell. While this is somewhat of a trivial result since the fuel

cell emulator is simply a voltage source with a resistor in series, an accurately sloping

voltage/current power source is required for characterizing motor performance with a

fuel cell power source. Additionally, with an emulator current of 60 A, and resistance

set to 0.55 Ω, the variable resistor dissipates around 2 kW of power. These tests prove

the cooling systems effectiveness in regulating resistor temperature and maintaining

constant resistance values for a wide range of emulated fuel cell currents.

36

0 10 20 30 40 50 60 7030

35

40

45

50

55

60

65

70

75


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

AXI5330DBL, APC 22 x 12, no fuselageAXI5330DBL, APC 22 x 12, fuselageAXI5345−14, APC 27 x 13, no fuselageAXI5345−14, APC 27 x 13, fuselageAXI5345−18, APC 24 x 12, no fuselageAXI5345−18, APC 24 x 12, fuselageAXI5360−20, APC 26 x 15, no fuselageAXI5360−20, APC 26 x 15, fuselageSimulation

Figure 5.1: Comparison of simulated polarization curve to experimental values forthe steady-state SOFC PNNL Model 08 emulator assuming operation in the ohmicregion

37

0 10 20 30 40 50 60 7030

35

40

45

50

55

60

65

70


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)



38

0 10 20 30 40 50 60 7030

35

40

45

50

55

60

65

70


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)



39

0 10 20 30 40 50 60 7030

35

40

45

50

55

60

65

70


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)



40

0 10 20 30 40 50 60 7035

40

45

50

55

60


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)



41

0 10 20 30 40 50 60 7040

45

50

55

60

65


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)



42

BLDC Motor Modeling Results

The propeller determines the relationship between motor speed and load torque.

If the propeller models used in the simulation program do not accurately describe

the propeller performance in the wind tunnel, comparison between simulated mo-

tor performance and wind tunnel motor performance is not effective. To eliminate

discrepancies between simulated and wind tunnel motor performance caused by in-

accuracies in the propeller models, a second order polynomial was fit to the recorded

torque and propeller speed values for each test. As indicated in equation 2.13, torque

is a function of air density, the propeller’s coefficient of power, propeller diameter and

propeller speed. Table 2.4 and Figure 2.7(a) show that this coefficient is accurately

described as a second order function of the advance ratio, the ratio of velocity and

propeller speed (equation 2.11). Assuming constant velocity, CP becomes a function

of propeller speed with the form

CP =α2

n2p

+α1

np+ α0 (5.1)

Combining this with equation 2.13, and assuming constant ρ, the relationship

between τ and ω takes the form

τ = α′0ω2 + α′1ω + α′2 (5.2)

Thus, fitting simulated models to measured results simply shifts the 2nd order

propeller model to match experimental data. Similarly, a 1st order polynomial is fit

to the emulator’s voltage and current data. This removes any differences in emulator

open circuit voltage and resistance from simulated models. For all polynomial fits,

the coefficient of determination, R2, values were greater than 0.99.

43

Figures 5.7 through 5.14 show experimental results for each BLDC motor system.

Each motor was tested with six combinations of fuel cell models and propellers. The

solid lines indicate the simulated relationships between fuel cell voltage and propeller

speed, and fuel cell current and motor torque using the method described above.

Since simulation variables Vm and Im are not directly measurable, performance of the

controller and motor are lumped together.

Wind tunnel tests show very good correlation to motor models. These tests en-

compass a variety of power source characteristics and load profiles with the simulation

program predicting motor performance in every test reasonably well.

The AXI double 5330/20, AXI 5345/14 and AXI 5345/18 motor models slightly

over-predict motor performance. That is, for a given fuel cell current, the simulation

program predicts a higher motor torque than is measured. Similarly, for a given motor

speed, the fuel cell emulator voltage is lower than the simulated fuel cell voltage. This

indicates a lower motor operating efficiency than predicted in simulation and tends

to be more predominant for low power operation and with the larger APC propellers.

The reduced efficiencies for low power operation is expected as all motors advertise

maximum efficiencies when current is in excess of 20 A. Additionally, the low power

levels correspond to low duty cycle numbers where switching losses in the motor

controller represent a higher percentage of total system losses. The simulation model

assumes a lossless controller.

The higher operating efficiencies with the APC 22 x 12 and 24 x 12 propellers was

also expected for the AXI 5345/14 and 5345/18 motors. These motors are smaller

than the 5360/20 and only rated for use with 22 in. and 24 in. propellers. However,

both the AXI double 5330/20 and the AXI 5360/20 are rated for large propellers so

higher operating efficiencies with the smaller props is somewhat surprising.

44

250

300

350

400

450

500

550

600

650

700

750

30354045505560657075

Sha

ft ro

tatio

nal v

eloc

ity (

Rad

ians

/sec

)

Voltage at fuel cell terminals (V)

PN

NL

Mod

el 0

8, A

PC

22

x 12

, no

fuse

lage

PN

NL

Mod

el 0

8, A

PC

22

x 12

, fus

elag

eS

imul

atio

nP

NN

L M

odel

09,

AP

C 2

7 x

13, n

o fu

sela

geP

NN

L M

odel

09,

AP

C 2

7 x

13, f

usel

age

Sim

ulat

ion

PN

NL

Mod

el 1

0, A

PC

22

x 12

, no

fuse

lage

PN

NL

Mod

el 1

0, A

PC

22

x 12

, fus

elag

eS

imul

atio

nP

NN

L M

odel

11,

AP

C 2

4 x

12, n

o fu

sela

geP

NN

L M

odel

11,

AP

C 2

4 x

12, f

usel

age

Sim

ulat

ion

PN

NL

Mod

el 1

2, A

PC

26

x 15

, no

fuse

lage

PN

NL

Mod

el 1

2, A

PC

26

x 15

, fus

elag

eS

imul

atio

nP

NN

L M

odel

13,

AP

C 2

7 x

13, n

o fu

sela

geP

NN

L M

odel

13,

AP

C 2

7 x

13, f

usel

age

Sim

ulat

ion

Fig

ure

5.7:

Com

par

ison

ofsi

mula

ted

volt

age-

spee

dre

lati

onsh

ips

for

the

AX

ID

BL

5330

/20

mot

orto

exp

erim

enta

lre

sult

s

45

010

2030

4050

6070

800

0.51

1.52

2.53

3.54

4.55

Cur

rent

at f

uel c

ell t

erm

inal

s (A

)

Torque on shaft (N−m)

PN

NL

Mod

el 0

8, A

PC

22

x 12

, no

fuse

lage

PN

NL

Mod

el 0

8, A

PC

22

x 12

, fus

elag

eS

imul

atio

nP

NN

L M

odel

09,

AP

C 2

7 x

13, n

o fu

sela

geP

NN

L M

odel

09,

AP

C 2

7 x

13, f

usel

age

Sim

ulat

ion

PN

NL

Mod

el 1

0, A

PC

22

x 12

, no

fuse

lage

PN

NL

Mod

el 1

0, A

PC

22

x 12

, fus

elag

eS

imul

atio

nP

NN

L M

odel

11,

AP

C 2

4 x

12, n

o fu

sela

geP

NN

L M

odel

11,

AP

C 2

4 x

12, f

usel

age

Sim

ulat

ion

PN

NL

Mod

el 1

2, A

PC

26

x 15

, no

fuse

lage

PN

NL

Mod

el 1

2, A

PC

26

x 15

, fus

elag

eS

imul

atio

nP

NN

L M

odel

13,

AP

C 2

7 x

13, n

o fu

sela

geP

NN

L M

odel

13,

AP

C 2

7 x

13, f

usel

age

Sim

ulat

ion

Fig

ure

5.8:

Com

par

ison

ofsi

mula

ted

torq

ue-

curr

ent

rela

tion

ship

sfo

rth

eA

XI

DB

L53

30/2

0m

otor

toex

per

imen

tal

resu

lts

46

250

300

350

400

450

500

550

600

650

700

750

303540455055606570

Sha

ft ro

tatio

nal v

eloc

ity (

Rad

ians

/sec

)


PN

NL

Mod

el 0

8, A

PC

27

x 13

, no

fuse

lage

PN

NL

Mod

el 0

8, A

PC

27

x 13

, fus

elag

eS

imul

atio

nP

NN

L M

odel

09,

AP

C 2

6 x

15, n

o fu

sela

geP

NN

L M

odel

09,

AP

C 2

6 x

15, f

usel

age

Sim

ulat

ion

PN

NL

Mod

el 1

0, A

PC

27

x 13

, no

fuse

lage

PN

NL

Mod

el 1

0, A

PC

27

x 13

, fus

elag

eS

imul

atio

nP

NN

L M

odel

11,

AP

C 2

2 x

12, n

o fu

sela

geP

NN

L M

odel

11,

AP

C 2

2 x

12, f

usel

age

Sim

ulat

ion

PN

NL

Mod

el 1

2, A

PC

24

x 12

, no

fuse

lage

PN

NL

Mod

el 1

2, A

PC

24

x 12

, fus

elag

eS

imul

atio

nP

NN

L M

odel

13,

AP

C 2

6 x

15, n

o fu

sela

geP

NN

L M

odel

13,

AP

C 2

6 x

15, f

usel

age

Sim

ulat

ion

Fig

ure

5.9:

Com

par

ison

ofsi

mula

ted

volt

age-

spee

dre

lati

onsh

ips

for

the

AX

I53

45/1

4m

otor

toex

per

imen

tal

resu

lts

47

010

2030

4050

600

0.51

1.52

2.53

3.54

4.5

Cur

rent

at f

uel c

ell t

erm

inal

s (A

)


PN

NL

Mod

el 0

8, A

PC

27

x 13

, no

fuse

lage

PN

NL

Mod

el 0

8, A

PC

27

x 13

, fus

elag

eS

imul

atio

nP

NN

L M

odel

09,

AP

C 2

6 x

15, n

o fu

sela

geP

NN

L M

odel

09,

AP

C 2

6 x

15, f

usel

age

Sim

ulat

ion

PN

NL

Mod

el 1

0, A

PC

27

x 13

, no

fuse

lage

PN

NL

Mod

el 1

0, A

PC

27

x 13

, fus

elag

eS

imul

atio

nP

NN

L M

odel

11,

AP

C 2

2 x

12, n

o fu

sela

geP

NN

L M

odel

11,

AP

C 2

2 x

12, f

usel

age

Sim

ulat

ion

PN

NL

Mod

el 1

2, A

PC

24

x 12

, no

fuse

lage

PN

NL

Mod

el 1

2, A

PC

24

x 12

, fus

elag

eS

imul

atio

nP

NN

L M

odel

13,

AP

C 2

6 x

15, n

o fu

sela

geP

NN

L M

odel

13,

AP

C 2

6 x

15, f

usel

age

Sim

ulat

ion

Fig

ure

5.10

:C

ompar

ison

ofsi

mula

ted

torq

ue-

curr

ent

rela

tion

ship

sfo

rth

eA

XI

5345

/14

mot

orto

exp

erim

enta

lre

sult

s

48

250

300

350

400

450

500

550

600

650

700

354045505560657075

Sha

ft ro

tatio

nal v

eloc

ity (

Rad

ians

/sec

)


PN

NL

Mod

el 0

8, A

PC

24

x 12

, no

fuse

lage

PN

NL

Mod

el 0

8, A

PC

24

x 12

, fus

elag

eS

imul

atio

nP

NN

L M

odel

09,

AP

C 2

2 x

12, n

o fu

sela

geP

NN

L M

odel

09,

AP

C 2

2 x

12, f

usel

age

Sim

ulat

ion

PN

NL

Mod

el 1

0, A

PC

24

x 12

, no

fuse

lage

PN

NL

Mod

el 1

0, A

PC

24

x 12

, fus

elag

eS

imul

atio

nP

NN

L M

odel

11,

AP

C 2

6 x

15, n

o fu

sela

geP

NN

L M

odel

11,

AP

C 2

6 x

15, f

usel

age

Sim

ulat

ion

PN

NL

Mod

el 1

2, A

PC

27

x 13

, no

fuse

lage

PN

NL

Mod

el 1

2, A

PC

27

x 13

, fus

elag

eS

imul

atio

nP

NN

L M

odel

13,

AP

C 2

2 x

12, n

o fu

sela

geP

NN

L M

odel

13,

AP

C 2

2 x

12, f

usel

age

Sim

ulat

ion

Fig

ure

5.11

:C

ompar

ison

ofsi

mula

ted

volt

age-

spee

dre

lati

onsh

ips

for

the

AX

I53

45/1

8m

otor

toex

per

imen

tal

resu

lts

49

010

2030

4050

60

0

0.51

1.52

2.53

3.54

4.5

Cur

rent

at f

uel c

ell t

erm

inal

s (A

)


PN

NL

Mod

el 0

8, A

PC

24

x 12

, no

fuse

lage

PN

NL

Mod

el 0

8, A

PC

24

x 12

, fus

elag

eS

imul

atio

nP

NN

L M

odel

09,

AP

C 2

2 x

12, n

o fu

sela

geP

NN

L M

odel

09,

AP

C 2

2 x

12, f

usel

age

Sim

ulat

ion

PN

NL

Mod

el 1

0, A

PC

24

x 12

, no

fuse

lage

PN

NL

Mod

el 1

0, A

PC

24

x 12

, fus

elag

eS

imul

atio

nP

NN

L M

odel

11,

AP

C 2

6 x

15, n

o fu

sela

geP

NN

L M

odel

11,

AP

C 2

6 x

15, f

usel

age

Sim

ulat

ion

PN

NL

Mod

el 1

2, A

PC

27

x 13

, no

fuse

lage

PN

NL

Mod

el 1

2, A

PC

27

x 13

, fus

elag

eS

imul

atio

nP

NN

L M

odel

13,

AP

C 2

2 x

12, n

o fu

sela

geP

NN

L M

odel

13,

AP

C 2

2 x

12, f

usel

age

Sim

ulat

ion

Fig

ure

5.12

:C

ompar

ison

ofsi

mula

ted

torq

ue-

curr

ent

rela

tion

ship

sfo

rth

eA

XI

5345

/18

mot

orto

exp

erim

enta

lre

sult

s

50

300

350

400

450

500

550

600

40455055606570

Sha

ft ro

tatio

nal v

eloc

ity (

Rad

ians

/sec

)


PN

NL

Mod

el 0

8, A

PC

26

x 15

, no

fuse

lage

PN

NL

Mod

el 0

8, A

PC

26

x 15

, fus

elag

eS

imul

atio

nP

NN

L M

odel

09,

AP

C 2

4 x

12, n

o fu

sela

geP

NN

L M

odel

09,

AP

C 2

4 x

12, f

usel

age

Sim

ulat

ion

PN

NL

Mod

el 1

0, A

PC

26

x 15

, no

fuse

lage

PN

NL

Mod

el 1

0, A

PC

26

x 15

, fus

elag

eS

imul

atio

nP

NN

L M

odel

11,

AP

C 2

7 x

13, n

o fu

sela

geP

NN

L M

odel

11,

AP

C 2

7 x

13, f

usel

age

Sim

ulat

ion

PN

NL

Mod

el 1

2, A

PC

22

x 12

, no

fuse

lage

PN

NL

Mod

el 1

2, A

PC

22

x 12

, fus

elag

eS

imul

atio

nP

NN

L M

odel

13,

AP

C 2

4 x

12, n

o fu

sela

geP

NN

L M

odel

13,

AP

C 2

4 x

12, f

usel

age

Sim

ulat

ion

Fig

ure

5.13

:C

ompar

ison

ofsi

mula

ted

volt

age-

spee

dre

lati

onsh

ips

for

the

AX

I53

60/2

0m

otor

toex

per

imen

tal

resu

lts

51

05

1015

2025

3035

4045

500

0.51

1.52

2.53

3.54

4.5

Cur

rent

at f

uel c

ell t

erm

inal

s (A

)


PN

NL

Mod

el 0

8, A

PC

26

x 15

, no

fuse

lage

PN

NL

Mod

el 0

8, A

PC

26

x 15

, fus

elag

eS

imul

atio

nP

NN

L M

odel

09,

AP

C 2

4 x

12, n

o fu

sela

geP

NN

L M

odel

09,

AP

C 2

4 x

12, f

usel

age

Sim

ulat

ion

PN

NL

Mod

el 1

0, A

PC

26

x 15

, no

fuse

lage

PN

NL

Mod

el 1

0, A

PC

26

x 15

, fus

elag

eS

imul

atio

nP

NN

L M

odel

11,

AP

C 2

7 x

13, n

o fu

sela

geP

NN

L M

odel

11,

AP

C 2

7 x

13, f

usel

age

Sim

ulat

ion

PN

NL

Mod

el 1

2, A

PC

22

x 12

, no

fuse

lage

PN

NL

Mod

el 1

2, A

PC

22

x 12

, fus

elag

eS

imul

atio

nP

NN

L M

odel

13,

AP

C 2

4 x

12, n

o fu

sela

geP

NN

L M

odel

13,

AP

C 2

4 x

12, f

usel

age

Sim

ulat

ion

Fig

ure

5.14

:C

ompar

ison

ofsi

mula

ted

torq

ue-

curr

ent

rela

tion

ship

sfo

rth

eA

XI

5360

/20

mot

orto

exp

erim

enta

lre

sult

s

52

The AXI 5360/20 model under predicts motor operation, though only slightly. It

is important to note however, that even with a maximum duty ratio of 1.0, this motor

cannot reach the PNNL dictated operation points when operating with any of the

studied propellers. Thus, the motor cannot turn the propeller at speeds required for

adequate thrust. This is reflected in comparing propeller speeds of the farthest most

right measured operating points of Figure 5.13 to those of Figures 5.7, 5.9 and 5.11.

Propeller Modeling Results

Equations, 2.12, 2.13 and 2.14 show that propeller torque and thrust are functions

of air density ρ, their respective dimensionless coefficients (CP and CT ), propeller

diameter L and propeller rotational speed np. Coefficients CP and CT are functions

of advance ratio, J , which itself is a function of simulated craft velocity, S, L and

np as explained in Table 2.4 and equation 2.11. Both ρ and S can vary between and

during propeller tests. Therefore, the most effective method for comparing measured

data to propeller models is to calculate J , CP and CT for all measured operating

points. Figures, 5.15 through 5.18 show these results.

The calculated CP for the APC 22 x 12, 24 x 12 and 27 x 13 propellers show fairly

good correlation to APC provided propeller models. These values tend to be slightly

higher than model values, but follow the same trend as a function of J . The calculated

CP values for the APC 26 x 15 propeller differ significantly from the model. CP can

be thought of as a measure of power required to turn a propeller at a specific advance

ratio. Compared to measured results, the simulation model grossly over predicts the

amount of power required for the APC 26 x 15 to spin. This is why the simulation

program predicts much lower thrust values for propulsion systems operating with this

propeller (see Appendix A for the full set of simulation results). Because measured CP

53

values for the other propellers correlate well with propeller models and the observed

CP values for the 26 x 15 prop are comparable to those of the other propellers, the

disparity between measured CP and the model is thought to be due to model error.

In all cases, the observed values of CT exceed model values for low J where pro-

peller speeds are high. This is largely due to a wind tunnel blockage effect discussed

in [20, 21]. In a limited air space environment such as a wind tunnel, higher static

pressures build aft of the propeller than upstream of the propeller. This exaggerates

thrust measurements with the effect more prominent at high propeller speeds.

54

0.25 0.3 0.35 0.40.02

0.022

0.024

0.026

0.028

0.03

0.032

Advance Ratio J = S/(nD)

Cal

cula

ted

Coe

ffici

ent o

f Pow

er (

CP)

PNNL Model 08, AXI5330DBL, no fuselagePNNL Model 08, AXI5330DBL, fuselagePNNL Model 09, AXI5345−18, no fuselagePNNL Model 09, AXI5345−18, fuselagePNNL Model 10, AXI5330DBL, no fuselagePNNL Model 10, AXI5330DBL, fuselagePNNL Model 11, AXI5345−14, no fuselagePNNL Model 11, AXI5345−14, fuselagePNNL Model 12, AXI5360−20, no fuselagePNNL Model 12, AXI5360−20, fuselagePNNL Model 13, AXI5345−18, no fuselagePNNL Model 13, AXI5345−18, fuselageSimulation

(a) Coefficient of Power (CP )

0.25 0.3 0.35 0.4

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

0.065


Cal

cula

ted

Coe

ffici

ent o

f Thr

ust (

CT)

PNNL Model 08, AXI5330DBL, no fuselagePNNL Model 08, AXI5330DBL, fuselagePNNL Model 09, AXI5345−18, no fuselagePNNL Model 09, AXI5345−18, fuselagePNNL Model 10, AXI5330DBL, no fuselagePNNL Model 10, AXI5330DBL, fuselagePNNL Model 11, AXI5345−14, no fuselagePNNL Model 11, AXI5345−14, fuselagePNNL Model 12, AXI5360−20, no fuselagePNNL Model 12, AXI5360−20, fuselagePNNL Model 13, AXI5345−18, no fuselagePNNL Model 13, AXI5345−18, fuselageSimulation

(b) Coefficient of Power (CT )

Figure 5.15: Comparison of simulated CP and CT values with experimental resultsfor the APC 22 in. x 12 in. propeller

55

0.25 0.3 0.35 0.4 0.450.014

0.016

0.018

0.02

0.022

0.024

0.026

0.028

0.03


Cal

cula

ted

Coe

ffici

ent o

f Pow

er (

CP)

PNNL Model 08, AXI5345−18, no fuselagePNNL Model 08, AXI5345−18, fuselagePNNL Model 09, AXI5360−20, no fuselagePNNL Model 09, AXI5360−20, fuselagePNNL Model 10, AXI5345−18, no fuselagePNNL Model 10, AXI5345−18, fuselagePNNL Model 11, AXI5330DBL, no fuselagePNNL Model 11, AXI5330DBL, fuselagePNNL Model 12, AXI5345−14, no fuselagePNNL Model 12, AXI5345−14, fuselagePNNL Model 13, AXI5360−20, no fuselagePNNL Model 13, AXI5360−20, fuselageSimulation


0.25 0.3 0.35 0.4 0.45

0.025

0.03

0.035

0.04

0.045

0.05

0.055


Cal

cula

ted

Coe

ffici

ent o

f Thr

ust (

CT)

PNNL Model 08, AXI5345−18, no fuselagePNNL Model 08, AXI5345−18, fuselagePNNL Model 09, AXI5360−20, no fuselagePNNL Model 09, AXI5360−20, fuselagePNNL Model 10, AXI5345−18, no fuselagePNNL Model 10, AXI5345−18, fuselagePNNL Model 11, AXI5330DBL, no fuselagePNNL Model 11, AXI5330DBL, fuselagePNNL Model 12, AXI5345−14, no fuselagePNNL Model 12, AXI5345−14, fuselagePNNL Model 13, AXI5360−20, no fuselagePNNL Model 13, AXI5360−20, fuselageSimulation



56

0.25 0.3 0.35 0.4 0.45

0.025

0.03

0.035

0.04

0.045


Cal

cula

ted

Coe

ffici

ent o

f Pow

er (

CP)

PNNL Model 08, AXI5360−20, no fuselagePNNL Model 08, AXI5360−20, fuselagePNNL Model 09, AXI5345−14, no fuselagePNNL Model 09, AXI5345−14, fuselagePNNL Model 10, AXI5360−20, no fuselagePNNL Model 10, AXI5360−20, fuselagePNNL Model 11, AXI5345−18, no fuselagePNNL Model 11, AXI5345−18, fuselagePNNL Model 12, AXI5330DBL, no fuselagePNNL Model 12, AXI5330DBL, fuselagePNNL Model 13, AXI5345−14, no fuselagePNNL Model 13, AXI5345−14, fuselageSimulation


0.25 0.3 0.35 0.4 0.45

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06


Cal

cula

ted

Coe

ffici

ent o

f Thr

ust (

CT)

PNNL Model 08, AXI5360−20, no fuselagePNNL Model 08, AXI5360−20, fuselagePNNL Model 09, AXI5345−14, no fuselagePNNL Model 09, AXI5345−14, fuselagePNNL Model 10, AXI5360−20, no fuselagePNNL Model 10, AXI5360−20, fuselagePNNL Model 11, AXI5345−18, no fuselagePNNL Model 11, AXI5345−18, fuselagePNNL Model 12, AXI5330DBL, no fuselagePNNL Model 12, AXI5330DBL, fuselagePNNL Model 13, AXI5345−14, no fuselagePNNL Model 13, AXI5345−14, fuselageSimulation



57

0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42

0.016

0.018

0.02

0.022

0.024

0.026


Cal

cula

ted

Coe

ffici

ent o

f Pow

er (

CP)

PNNL Model 08, AXI5345−14, no fuselagePNNL Model 08, AXI5345−14, fuselagePNNL Model 09, AXI5330DBL, no fuselagePNNL Model 09, AXI5330DBL, fuselagePNNL Model 10, AXI5345−14, no fuselagePNNL Model 10, AXI5345−14, fuselagePNNL Model 11, AXI5360−20, no fuselagePNNL Model 11, AXI5360−20, fuselagePNNL Model 12, AXI5345−18, no fuselagePNNL Model 12, AXI5345−18, fuselagePNNL Model 13, AXI5330DBL, no fuselagePNNL Model 13, AXI5330DBL, fuselageSimulation


0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42

0.02

0.025

0.03

0.035

0.04

0.045

0.05


Cal

cula

ted

Coe

ffici

ent o

f Thr

ust (

CT)

PNNL Model 08, AXI5345−14, no fuselagePNNL Model 08, AXI5345−14, fuselagePNNL Model 09, AXI5330DBL, no fuselagePNNL Model 09, AXI5330DBL, fuselagePNNL Model 10, AXI5345−14, no fuselagePNNL Model 10, AXI5345−14, fuselagePNNL Model 11, AXI5360−20, no fuselagePNNL Model 11, AXI5360−20, fuselagePNNL Model 12, AXI5345−18, no fuselagePNNL Model 12, AXI5345−18, fuselagePNNL Model 13, AXI5330DBL, no fuselagePNNL Model 13, AXI5330DBL, fuselageSimulation



58

Measurement Uncertainty

In the wind tunnel experiments, there are two primary mechanisms for measure-

ment uncertainty. First, as was mentioned in the Instruments section of the previous

chapter, each instrument has an associated amount of measurement uncertainty. Sec-

ond, the turbulent air flow in the wind tunnel causes stochastic fluctuations in air

velocity, which causes stochastic fluctuations in all data measurements. Table 5.1

below gives confidence intervals (i.e. 95% of measurements within the interval) for

the directly measurable quantities.

Table 5.1: The uncertainty in measurements is due to a combination of instrumentlimitations and system noise primarily caused by turbulent air flow through the windtunnel. This table lists the 95% confidence intervals for each measured quantity.

Measurement Confidence IntervalWind Tunnel Air Velocity (S) ±2 m/sFuel Cell Emulator Current (Ic) ±0.2 AFuel Cell Emulator Voltage (Vc) ±0.3 VDuty Cycle (D) ±0.005Motor/Propeller Speed (ω) ±1 rad/sMotor Torque (τ) ±0.1 N-mPropeller Thrust (T ) ±3 N

For the fuel cell emulator and BLDC system results, error analyses of collected

data are determined directly from the confidence intervals of table 5.1. This is be-

cause the data presented in their analyses are all directly measurable quantities. The

propeller analysis is more complicated as results are expressed in calculations of CT

and CP as functions of J . These calculations require two or more measurements each

with an associated amount of uncertainty. To determine the total uncertainty in the

calculated values of CT , CP and J , the uncertainty analysis method presented in [22]

is used. In this method, the uncertainty in the calculated result F where F is a

59

function of independent variables, x1, x2, ..., xn, each with an associated measure of

uncertainty, w1, w2, ..., wn, is determined by the formula

wF =

((∂F

∂x1

w1

)2

+

(∂F

∂x2

w2

)2

+ ...+

(∂F

∂xnwn

)2)1/2

(5.3)

Using the confidence intervals of table 5.1 as the measures of uncertainty, confi-

dence intervals for each calculated value of J , CP and CT are found. These results are

included in Appendix B along with the calculated values of J , CP and CT . Noting

these results, we see that the variability in the operation points seen in the propeller

results, i.e. figures 5.15 through 5.18 is easily explained. First, primarily due to tur-

bulent air flow, J is found to have confidence intervals ranging from ±0.04 to ±0.07

with the larger intervals corresponding to larger J . This indicates that data points

shown in figures 5.15 through 5.18 could vary fairly significantly along the horizontal

axis, especially for higher values of J . Similarly, CT and CP have relatively large

confidence intervals also corresponding to higher values of J . This is primarily due

to inherent uncertainty in instrument measurements. High values of J correspond

to low propeller speeds, and thus, small measurements of thrust and torque. The

inherent inaccuracies of the Cooper LXT-920 load cell are significant in magnitude

compared to the thrust and torque values recorded for these operation points. Thus,

as is reflected in the figures, calculated values of CT and CP show large variances

especially for high values of J .

Despite these variations, the general trends of CP and CT as functions of J match

model expectations. Additionally, little appreciable difference in propeller perfor-

mance is seen between tests with and without the mock fuselage installed. These

results give some confidence that component models (with the exception of the CP

values for the APC 26 x 15 propeller) are accurate.

60

It is important to note that this error analysis only serves to quantify error present

in data measurements caused by measurement uncertainty. Other mechanisms of

error such as the wind tunnel blockage effect mentioned earlier cause offset deviations

in measured quantities from model predictions. Further, this error analysis assumes

variable uncertainties to be independent, which is obviously not the case for the

stochastic fluctuations in all data measurements caused by turbulent air flow. Still,

the results of the error analysis are consistent with the number of significant digits

presented in data tables of Appendix B and provides further insight into the variability

seen in wind tunnel testing.

61

CONCLUSION

In this thesis, a physically-based model for design and optimization of a fuel cell

powered UAV electric propulsion system comprised of a solid oxide fuel cell providing

power, a brushless DC motor and controller, and a propeller was presented. The

individual component models were integrated into a simulation program which used

the MATLAB command fsolve() to numerically find specific propulsion operating

points. A graphical procedure using this simulation program was introduced that

allows rapid assessment and selection of design choices, including fuel cell character-

istics and hybridization with multiple sources. Experimental results from wind tunnel

tests provided validation of the component models.

In addition to providing insight into design choices, the graphical presentation

of simulation results such as Figure 3.1 proved to be very effective for coordinating

the efforts of multiple groups involved in building a fuel cell / electric propulsion

system. Stack designers could immediately appreciate the implications of increasing

the height of the stack or changing cell thickness, simply by sketching a new fuel cell

curve on the plot. Further, the effect of power source hybridization or alternate power

electronic topologies can be displayed on the same graph by adding the associated

curves to the plot as in Figure 3.3. Finally, the implications of design changes in the

fuel cell / electric propulsion are immediately apparent to the air frame design team.

Future Work

There are a couple remaining concerns and important goals for future work in

this project. Though wind tunnel test results give some confidence that a UAV uti-

lizing a propulsion system designed with the simulation program will fly, variations

62

in measured propeller performance from model values exist. Further, wind tunnel

air flow velocities measure only around 40% of specified UAV velocity so propulsion

system performance at higher velocities must be extrapolated from these experimen-

tal results. To alleviate remaining concerns, it is recommended that propeller tests

take place in a fully calibrated wind tunnel such as the Kirsten Wind Tunnel at the

University of Washington. The working section of this wind tunnel is 2.4 m x 3.7 m in

cross-sectional area which should significantly reduce the wind tunnel blockage effect

described in chapter five. Additionally, the wind tunnel’s low turbulence intensity

factor would reduce measurement fluctuations and with maximum velocities of 90

m/s, the wind tunnel easily meets UAV velocity specifications.

For future studies, further design investigations should center around dynamic

models, which can be combined with aircraft dynamic models for a fully integrated

UAV simulation program. Also, investigation into a hybrid power source is required

to increase the operation range of the propulsion system as illustrated in Figure 3.3.

In addition to increasing maximum propulsion system thrust, a second power source

could also be utilized to protect the fuel cell from exposure to severe high-current

loading and load transients.

63

REFERENCES CITED

64

[1] T.J. Becker. Flying on Hydrogen: Georgia Tech Researchers Use Fuel Cells toPower Unmanned Aerial Vehicle. Research News & Publication Office, GeorgiaInstitute of Technology, August 2006.

[2] E. Lafey. U-M Students Set Fuel-Cell Airplane Flight Record. Chicago Tribune,November 2008.

[3] S. Kearns, M. Yu. Cal State L.A.’s Fuel-Cell Plane Passes Key Flight Test. CSUNewsline California State University-L.A., September 2006.

[4] U. C. Ofoma, C. C. Wu. Design of a Fuel Cell Powered UAV for EnvironmentalResearch. AIAA 3rd Unmanned Unlimited Technical Conference, Workshop andExhibit, 2004.

[5] D. S. Soban, E. Upton. Design of a UAV to Optimize Use of Fuel Cell PropulsionTechnology. Infotech@aerospace, 2005.

[6] B. A. Moffitt, T. H. Bradley, D. E.Parekh, D. Mavris. Design and PerformanceValidation of a Fuel Cell Unmanned Aerial Vehicle. 44th AIAA Aerospace Sci-ences Meeting and Exhibit, 2006.

[7] T. H. Bradley, B. A. Moffitt, D. E.Parekh, D. Mavris. Flight Test Results for aFuel Cell Unmanned Aerial Vehicle. 45th AIAA Aerospace Sciences Meeting andExhibit, 2007.

[8] P. Lindahl, E. Moog, S. Shaw. Simulation, Design, and Validation of a UAVSOFC Propulsion System. IEEE Aerospace Conference, 2009.

[9] EG&G Technical Services, Inc. Fuel Cell Handbook Seventh Edition. U.S. De-partment of Energy, 2004.

[10] B. Viswanathan, M. Aulice Scibioh. Fuel Cells Principles and Applications. CRCPress, Taylor & Francis Group, 2007.

[11] S. Pasricha, S. R. Shaw. A Dynamic PEM Fuel Cell Model. IEEE Transactionson Energy Conversion, 21:484–490, June 2006.

[12] Caisheng Wang, M. Hashem Nehrir. A Physically Based Dynamic Model forSolid Oxide Fuel Cells. IEEE Transactions on Energy Conversion, 22(4):887–897, December 2007.

[13] S. Ogasawara, H. Akagi. An Approach to Position Sensorless Drive for BrushlessDC Motors. IEEE Transactions on Industry Applications, 27:928–933, Sept.-Oct.1991.

http://gtresearchnews.gatech.edu/newsrelease/fuel-cell-aircraft.htm

http://gtresearchnews.gatech.edu/newsrelease/fuel-cell-aircraft.htm

http://archives.chicagotribune.com/2008/nov/17/science/chi-ap-mi-exchange-fuelcell

http://www.calstate.edu/newsline/2006/n20060901la1.shtml

65

[14] C. G. Kim, J. H. Lee, H. W. Kim, M. J. Youn. Study on Maximum TorqueGeneration For Sensorless Controlled Brushless DC Motor With TrapezoidalBack EMF. Electric Power Applications, IEEE Proceedings, 152:277–291, March2005.

[15] P. Yedamale. Brushless DC (BLDC) Motor Fundamentals. Technical Report,Microchip Technologies, 2003.

[16] H. A. Toliyat, G. B. Kliman, editors. Handbook of Electric Motors. Taylor &Francis Group, 2004.

[17] Pragasen Pillay, Ramu Krishnan. Modeling, Simulation, and Analysis ofPermanent-Magnet Motor Drives, PartII: The Brushless DC Motor Drive. IEEETransactions on Industry Applications, 25(2):274–279, March/April 1989.

[18] B. W. McCormick. Aerodynamics, Aeronautics, and Flight Mechanics. JohnWiley & Sons, 1979.

[19] R. D. Mehta, P. Bradshaw. Design Rules for Small Low Speed Wind Tunnels.Aeronautical Journal of the Royal Aeronautical Society, pages 443–449, Novem-ber 1979.

[20] R. E. Fitzgerald. Wind Tunnel Blockage Corrections for Propellers. Master’sThesis, University of Maryland, 2007.

[21] E. K. Corrigan IV. Survey of Small Unmanned Aerial Vehicle Electric PropulsionSystem. Master’s Thesis, University of Dayton, 2007.

[22] J. P. Holmes. Experimental Methods for Engineers. McGraw-Hill, Inc., 1994.

66

APPENDICES

67

APPENDIX A

SIMULATION RESULTS

68

Appendix A contains the full set of simulation results for all combinations of

propulsion system components used in this study as indicated by Figure 2.1. The

SOFC stack models and their associated parameters are listed in Table 2.2, the BLDC

motors in Table 2.3, and the propellers in Table 2.4. The blue line in the figures below

represent the linearized fuel cell stack, the dashed black lines indicate constant thrust

values, and the red box defines a family of voltage/current curves for the motor and

propeller combination. The physically based models used in the simulation program

and the simulation program itself are described in chapters two and three, respectively.

In all cases, the motor controller was treated as a lossless component. Air density

was assumed to be 1.2 kg/m3 and cruising velocity, 31.3 m/s.

69

Solid Oxide Fuel Cell Model 8

AXI 5330 DBL BLDC Motor

10 20 30 40 50 600

10

20

30

40

50

60

70

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60

70

Current at fuel cell terminals (A)V

olta

ge a

t fue

l cel

l ter

min

als

(V)

39.1 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

28.8 N20 N

35 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

10

20

30

40

50

60


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.8 N20 N

35 N50 N

(d) APC 27 in. x 13 in.

Figure A.1: Simulation results for the propulsion system with components: SOFCModel 8, AXI 5330 DBL Motor, and Jeti Spin 99 Controller. The propeller is indicatedbelow each figure.

70

AXI Motor 5345-14 BLDC Motor

10 20 30 40 50 600

20

40

60

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.8 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60

70

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.9 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

29 N20 N35 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

10

20

30

40

50

60

70


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.3 N

20 N35 N

50 N

(d) APC 27 in. x 13 in.

Figure A.2: Simulation results for the propulsion system with components: SOFCModel 8, AXI 5345-14 Motor, and Jeti Spin 99 Controller. The propeller is indicatedbelow each figure.

71


10 20 30 40 50 600

20

40

60

80

100

120


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.9 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

20

40

60

80

100


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

40 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60

70

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

29.3 N

20 N35 N

50 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

20

40

60

80

100


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.6 N

20 N35 N

50 N

(d) APC 27 in. x 13 in.


72

AXI Motor 5360 BLDC Motor

10 20 30 40 50 600

50

100

150

200


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

37.2 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

50

100

150


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.5 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

20

40

60

80

100

120


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

28.9 N

20 N35 N

50 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

50

100

150


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.6 N

20 N35 N

50 N

(d) APC 27 in. x 13 in.

Figure A.4: Simulation results for the propulsion system with components: SOFCModel 8, AXI 5360 Motor, and Jeti Spin 99 Controller. The propeller is indicatedbelow each figure.

73



10 20 30 40 50 600

10

20

30

40

50

60

70

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

37.2 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60

70


olta

ge a

t fue

l cel

l ter

min

als

(V)

38.3 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

28.1 N20 N35 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

10

20

30

40

50

60


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38 N

20 N35 N

50 N

(d) APC 27 in. x 13 in.

Figure A.5: Simulation results for the propulsion system with components: SOFCModel 9, AXI 5330 DBL Motor, and Jeti Spin 99 Controller. The propeller is indicatedbelow each figure.

74


10 20 30 40 50 600

20

40

60

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.1 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60

70

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.1 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

28.3 N20 N

35 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

10

20

30

40

50

60

70


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.5 N

20 N35 N

50 N

(d) APC 27 in. x 13 in.


75


10 20 30 40 50 600

20

40

60

80

100

120


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.1 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

20

40

60

80

100


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.2 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60

70

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

28.5 N

20 N35 N

50 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

20

40

60

80

100


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.7 N

20 N35 N

50 N

(d) APC 27 in. x 13 in.


76


10 20 30 40 50 600

50

100

150

200


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

36.4 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

50

100

150


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

37.7 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

20

40

60

80

100

120


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

28.2 N

20 N35 N

50 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

50

100

150


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

37.7 N

20 N35 N

50 N

(d) APC 27 in. x 13 in.


77



10 20 30 40 50 600

10

20

30

40

50

60

70

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

37.8 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60

70


olta

ge a

t fue

l cel

l ter

min

als

(V)

38.9 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

28.6 N

20 N35 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

10

20

30

40

50

60


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.6 N

20 N35 N

50 N

(d) APC 27 in. x 13 in.

Figure A.9: Simulation results for the propulsion system with components: SOFCModel 10, AXI 5330 DBL Motor, and Jeti Spin 99 Controller. The propeller isindicated below each figure.

78


10 20 30 40 50 600

20

40

60

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.7 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60

70

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.7 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

28.8 N

20 N35 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

10

20

30

40

50

60

70


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.2 N

20 N35 N

50 N

(d) APC 27 in. x 13 in.


79


10 20 30 40 50 600

20

40

60

80

100

120


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.7 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

20

40

60

80

100


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.8 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60

70

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

29.1 N

20 N35 N

50 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

20

40

60

80

100


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.4 N

20 N35 N

50 N

(d) APC 27 in. x 13 in.


80


10 20 30 40 50 600

50

100

150

200


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

37 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

50

100

150


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.4 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

20

40

60

80

100

120


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

28.7 N

20 N35 N

50 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

50

100

150


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.4 N

20 N35 N

50 N

(d) APC 27 in. x 13 in.


81



10 20 30 40 50 600

10

20

30

40

50

60

70

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

37.9 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60

70


olta

ge a

t fue

l cel

l ter

min

als

(V)

39 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

28.7 N20 N35 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

10

20

30

40

50

60


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.7 N

20 N35 N

50 N

(d) APC 27 in. x 13 in.


82


10 20 30 40 50 600

20

40

60

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.7 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60

70

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.8 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

28.9 N20 N

35 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

10

20

30

40

50

60

70


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.2 N

20 N35 N

50 N

(d) APC 27 in. x 13 in.


83


10 20 30 40 50 600

20

40

60

80

100

120


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.8 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

20

40

60

80

100


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.9 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60

70

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

29.2 N

20 N35 N

50 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

20

40

60

80

100


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.4 N

20 N35 N

50 N

(d) APC 27 in. x 13 in.


84


10 20 30 40 50 600

50

100

150

200


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

37.1 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

50

100

150


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.4 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

20

40

60

80

100

120


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

28.8 N

20 N35 N

50 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

50

100

150


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.5 N

20 N35 N

50 N

(d) APC 27 in. x 13 in.


85



10 20 30 40 50 600

10

20

30

40

50

60

70

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

37.9 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60

70


olta

ge a

t fue

l cel

l ter

min

als

(V)

39 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

28.7 N20 N35 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

10

20

30

40

50

60


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.7 N20 N

35 N50 N

(d) APC 27 in. x 13 in.


86


10 20 30 40 50 600

20

40

60

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.8 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60

70

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.8 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

28.9 N20 N35 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

10

20

30

40

50

60

70


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.2 N

20 N35 N

50 N

(d) APC 27 in. x 13 in.


87


10 20 30 40 50 600

20

40

60

80

100

120


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.8 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

20

40

60

80

100


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.9 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60

70

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

29.2 N

20 N35 N

50 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

20

40

60

80

100


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.5 N

20 N35 N

50 N

(d) APC 27 in. x 13 in.


88


10 20 30 40 50 600

50

100

150

200


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

37.1 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

50

100

150


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.4 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

20

40

60

80

100

120


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

28.8 N

20 N35 N

50 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

50

100

150


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.5 N

20 N35 N

50 N

(d) APC 27 in. x 13 in.


89



10 20 30 40 50 600

10

20

30

40

50

60

70

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

37.9 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60

70


olta

ge a

t fue

l cel

l ter

min

als

(V)

39 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50


Vol

tage

at f

uel c

ell t

erm

inal

s (V

) 28.7 N

20 N35 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

10

20

30

40

50

60


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.8 N20 N35 N

50 N

(d) APC 27 in. x 13 in.


90


10 20 30 40 50 600

20

40

60

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.8 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60

70

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.8 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

28.9 N20 N

35 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

10

20

30

40

50

60

70


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.3 N20 N

35 N50 N

(d) APC 27 in. x 13 in.


91


10 20 30 40 50 600

20

40

60

80

100

120


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.8 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

20

40

60

80

100


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.9 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

10

20

30

40

50

60

70

80


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

29.2 N

20 N35 N

50 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

20

40

60

80

100


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

39.5 N

20 N35 N

50 N

(d) APC 27 in. x 13 in.


92


10 20 30 40 50 600

50

100

150

200


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

37.1 N

20 N35 N

50 N

(a) APC 22 in. x 12 in.

10 20 30 40 50 600

50

100

150


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.5 N

20 N35 N

50 N

(b) APC 22 in. x 12 in.

10 20 30 40 50 600

20

40

60

80

100

120


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

28.8 N

20 N35 N

50 N

(c) APC 26 in. x 15 in.

10 20 30 40 50 600

50

100

150


Vol

tage

at f

uel c

ell t

erm

inal

s (V

)

38.5 N

20 N35 N

50 N

(d) APC 27 in. x 13 in.


93

APPENDIX B

WIND TUNNEL TEST RESULTS

94

Appendix B lists the data gathered in the wind tunnel tests along with calcu-

lated values of J , CT and CP . These calculations assume data measurements with a

minimum of 2 significant digits.

95

Tab

leB

.1:

Win

dT

unnel

Dat

afo

rSO

FC

Model

08,

AX

ID

ouble

5330

/20

Mot

or,

AP

C22

x12

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.20

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.21

66.0

7.6

0.9

1237

812

0.35±

0.06

0.02

9±0.

007

0.02

5±0.

003

0.31

62.3

14.7

1.6

2646

212

0.30±

0.05

0.04

2±0.

005

0.02

8±0.

002

0.43

56.0

26.3

2.3

4454

013

0.27±

0.04

0.05

1±0.

004

0.03

0±0.

001

0.55

49.7

38.0

2.7

5458

413

0.25±

0.04

0.05

4±0.

003

0.03

0±0.

001

0.66

44.0

48.4

3.0

6261

113

0.24±

0.04

0.05

6±0.

003

0.03

1±0.

001

0.80

38.0

59.1

3.2

6762

213

0.23±

0.04

0.05

8±0.

003

0.03

1±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.20

66.5

6.9

0.9

1237

512

0.35±

0.06

0.02

9±0.

007

0.02

4±0.

003

0.31

62.3

14.6

1.6

2846

112

0.29±

0.05

0.04

4±0.

005

0.02

8±0.

002

0.45

55.9

26.4

2.3

4554

012

0.25±

0.04

0.05

2±0.

004

0.03

0±0.

001

0.55

49.6

37.6

2.8

5658

413

0.24±

0.04

0.05

5±0.

003

0.03

1±0.

001

0.67

43.9

48.4

3.0

6360

813

0.23±

0.04

0.05

8±0.

003

0.03

1±0.

001

0.80

37.8

59.4

3.2

6862

213

0.23±

0.04

0.05

9±0.

003

0.03

1±0.

001

96

Tab

leB

.2:

Win

dT

unnel

Dat

afo

rSO

FC

Model

08,

AX

ID

ouble

5345

/14

Mot

or,

AP

C27

x13

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.18

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.23

66.1

7.5

1.2

1630

813

0.38±

0.06

0.02

6±0.

005

0.01

8±0.

002

0.31

61.7

15.7

2.1

3437

013

0.31±

0.05

0.03

8±0.

003

0.02

1±0.

001

0.38

58.5

21.6

2.6

4440

012

0.28±

0.05

0.04

2±0.

003

0.02

2±0.

001

0.45

54.0

30.0

3.0

5542

914

0.30±

0.04

0.04

5±0.

002

0.02

3±0.

001

0.53

48.3

40.4

3.5

6545

014

0.28±

0.04

0.04

9±0.

002

0.02

4±0.

001

0.61

43.4

49.5

3.7

7046

314

0.27±

0.04

0.05

0±0.

002

0.02

4±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.24

66.1

7.5

1.2

1930

713

0.38±

0.06

0.03

0±0.

005

0.01

8±0.

002

0.31

61.6

15.7

2.1

3637

112

0.30±

0.05

0.03

9±0.

003

0.02

1±0.

001

0.38

58.5

21.5

2.6

4540

013

0.30±

0.05

0.04

2±0.

003

0.02

2±0.

001

0.43

54.0

30.0

3.1

5642

913

0.27±

0.04

0.04

6±0.

002

0.02

3±0.

001

0.53

48.4

40.2

3.4

6445

114

0.29±

0.04

0.04

7±0.

002

0.02

3±0.

001

0.63

42.4

51.0

3.7

7046

414

0.27±

0.04

0.05

0±0.

002

0.02

4±0.

001

97

Tab

leB

.3:

Win

dT

unnel

Dat

afo

rSO

FC

Model

08,

AX

ID

ouble

5345

/18

Mot

or,

AP

C24

x12

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.18

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.31

66.4

6.9

1.1

1834

813

0.38±

0.06

0.03

7±0.

006

0.02

2±0.

002

0.43

62.7

14.0

1.8

3542

113

0.31±

0.05

0.04

8±0.

004

0.02

5±0.

001

0.56

56.6

25.3

2.4

5348

613

0.27±

0.04

0.05

4±0.

003

0.02

6±0.

001

0.67

51.7

34.1

2.8

5951

813

0.25±

0.04

0.05

3±0.

003

0.02

6±0.

001

0.79

46.7

43.5

3.1

6054

113

0.25±

0.04

0.04

9±0.

003

0.02

6±0.

001

0.91

42.5

51.2

3.3

6355

213

0.24±

0.04

0.05

0±0.

002

0.02

7±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.32

66.4

6.9

1.0

1934

813

0.38±

0.06

0.03

9±0.

006

0.02

2±0.

002

0.43

62.1

15.0

1.8

3642

612

0.29±

0.05

0.04

8±0.

004

0.02

5±0.

001

0.55

56.6

25.1

2.5

5348

612

0.26±

0.04

0.05

4±0.

003

0.02

6±0.

001

0.67

51.7

34.1

2.8

5852

013

0.25±

0.04

0.05

2±0.

003

0.02

6±0.

001

0.80

46.7

43.4

3.2

6354

012

0.23±

0.04

0.05

2±0.

002

0.02

7±0.

001

0.91

42.5

51.0

3.3

6655

313

0.24±

0.04

0.05

2±0.

002

0.02

7±0.

001

98

Tab

leB

.4:

Win

dT

unnel

Dat

afo

rSO

FC

Model

08,

AX

ID

ouble

5360

/20

Mot

or,

AP

C26

x15

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.20

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.43

65.4

8.8

1.6

1931

014

0.42±

0.06

0.03

4±0.

005

0.02

8±0.

002

0.56

61.5

16.3

2.4

3536

512

0.32±

0.05

0.04

5±0.

004

0.03

0±0.

001

0.68

57.5

23.5

3.0

4740

113

0.31±

0.05

0.05

0±0.

003

0.03

1±0.

001

0.80

53.0

31.7

3.5

5842

814

0.30±

0.04

0.05

4±0.

003

0.03

1±0.

001

0.90

49.3

38.8

3.8

6444

513

0.28±

0.04

0.05

6±0.

003

0.03

2±0.

001

1.00

45.8

45.0

4.0

6945

614

0.29±

0.04

0.05

7±0.

002

0.03

2±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.43

65.4

8.6

1.6

2130

811

0.35±

0.06

0.03

8±0.

006

0.02

8±0.

002

0.55

61.5

15.8

2.4

3536

213

0.35±

0.05

0.04

6±0.

004

0.03

0±0.

001

0.67

57.6

23.2

3.0

4839

913

0.30±

0.05

0.05

2±0.

003

0.03

1±0.

001

0.78

53.5

30.7

3.4

5742

513

0.30±

0.04

0.05

4±0.

003

0.03

1±0.

001

0.91

49.3

38.5

3.8

6444

314

0.31±

0.04

0.05

7±0.

003

0.03

2±0.

001

1.00

45.7

45.1

4.0

6945

414

0.29±

0.04

0.05

8±0.

002

0.03

2±0.

001

99

Tab

leB

.5:

Win

dT

unnel

Dat

afo

rSO

FC

Model

09,

AX

ID

ouble

5330

/20

Mot

or,

AP

C27

x13

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.20

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.20

63.4

7.7

1.3

1331

012

0.36±

0.06

0.02

0±0.

005

0.01

8±0.

001

0.31

56.3

20.6

2.4

3738

912

0.29±

0.05

0.03

6±0.

003

0.02

2±0.

001

0.44

48.6

34.8

3.2

5443

613

0.28±

0.04

0.04

2±0.

002

0.02

3±0.

001

0.56

40.4

49.8

3.6

6245

914

0.27±

0.04

0.04

4±0.

002

0.02

4±0.

001

0.67

34.5

60.5

3.8

6546

613

0.26±

0.04

0.04

5±0.

002

0.02

4±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.20

63.6

7.6

1.3

1531

012

0.35±

0.06

0.02

4±0.

005

0.01

9±0.

001

0.31

56.4

20.8

2.4

3839

013

0.31±

0.05

0.03

8±0.

003

0.02

2±0.

001

0.44

48.6

34.8

3.2

5543

613

0.27±

0.04

0.04

3±0.

002

0.02

3±0.

001

0.55

40.3

50.0

3.7

6345

913

0.26±

0.04

0.04

5±0.

002

0.02

4±0.

001

0.67

34.5

60.5

3.8

6746

614

0.27±

0.04

0.04

6±0.

002

0.02

4±0.

001

100

Tab

leB

.6:

Win

dT

unnel

Dat

afo

rSO

FC

Model

09,

AX

ID

ouble

5345

/14

Mot

or,

AP

C26

x15

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.18

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.24

63.0

8.0

1.3

1829

212

0.40±

0.07

0.03

7±0.

006

0.02

6±0.

002

0.32

57.6

18.0

2.3

3536

013

0.35±

0.05

0.04

7±0.

004

0.02

9±0.

001

0.41

53.5

25.4

2.8

4539

313

0.31±

0.05

0.05

2±0.

003

0.03

0±0.

001

0.53

45.8

39.7

3.4

5942

812

0.27±

0.04

0.05

7±0.

003

0.03

1±0.

001

0.63

40.3

49.5

3.6

6443

813

0.28±

0.04

0.05

9±0.

003

0.03

2±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.24

63.0

8.0

1.3

1929

213

0.41±

0.07

0.04

0±0.

006

0.02

6±0.

002

0.33

57.6

17.9

2.3

3636

112

0.32±

0.05

0.04

8±0.

004

0.02

9±0.

001

0.43

52.5

27.5

2.9

4940

014

0.33±

0.05

0.05

4±0.

003

0.03

0±0.

001

0.53

45.9

39.6

3.4

5942

613

0.28±

0.04

0.05

8±0.

003

0.03

1±0.

001

0.63

40.4

49.7

3.6

6443

814

0.31±

0.04

0.05

9±0.

003

0.03

1±0.

001

101

Tab

leB

.7:

Win

dT

unnel

Dat

afo

rSO

FC

Model

09,

AX

ID

ouble

5345

/18

Mot

or,

AP

C22

x12

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.18

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.31

64.3

5.7

0.8

1136

213

0.36±

0.06

0.02

9±0.

008

0.02

3±0.

003

0.44

61.5

10.8

1.3

2243

213

0.30±

0.05

0.04

0±0.

006

0.02

6±0.

002

0.55

57.0

19.0

1.9

3650

712

0.25±

0.04

0.04

9±0.

004

0.02

8±0.

002

0.68

52.8

26.9

2.3

4654

913

0.24±

0.04

0.05

2±0.

003

0.02

9±0.

001

0.80

48.3

35.2

2.6

5357

913

0.24±

0.04

0.05

4±0.

003

0.03

0±0.

001

0.91

44.4

42.5

2.8

5859

913

0.23±

0.04

0.05

6±0.

003

0.03

0±0.

001

1.00

40.7

49.3

2.9

6260

914

0.23±

0.04

0.05

7±0.

003

0.03

0±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.32

64.3

5.6

0.8

1536

214

0.38±

0.06

0.04

0±0.

008

0.02

3±0.

003

0.44

61.5

10.8

1.3

2543

214

0.32±

0.05

0.04

6±0.

006

0.02

7±0.

002

0.55

56.9

19.0

1.9

4050

612

0.25±

0.04

0.05

3±0.

004

0.02

8±0.

002

0.67

52.8

27.2

2.3

4955

013

0.24±

0.04

0.05

6±0.

003

0.02

9±0.

001

0.78

48.4

35.4

2.6

5757

912

0.22±

0.04

0.05

8±0.

003

0.03

0±0.

001

0.91

44.2

42.5

2.8

6259

912

0.21±

0.04

0.06

0±0.

003

0.03

0±0.

001

1.00

40.7

49.1

2.9

6560

713

0.22±

0.04

0.06

1±0.

003

0.03

1±0.

001

102

Tab

leB

.8:

Win

dT

unnel

Dat

afo

rSO

FC

Model

09,

AX

ID

ouble

5360

/20

Mot

or,

AP

C24

x12

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.20

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.43

64.4

5.6

0.9

1232

713

0.40±

0.06

0.02

6±0.

007

0.02

1±0.

002

0.55

62.0

10.1

1.5

2338

313

0.36±

0.05

0.03

8±0.

005

0.02

4±0.

002

0.67

58.9

15.8

2.0

3443

413

0.30±

0.05

0.04

3±0.

004

0.02

6±0.

001

0.80

55.6

22.0

2.4

4447

013

0.28±

0.04

0.04

8±0.

003

0.02

7±0.

001

0.90

52.4

28.0

2.7

5649

713

0.27±

0.04

0.05

4±0.

003

0.02

7±0.

001

1.00

49.4

33.6

3.0

6051

614

0.27±

0.04

0.05

4±0.

003

0.02

7±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.44

64.4

5.6

0.9

1332

612

0.37±

0.06

0.02

9±0.

007

0.02

1±0.

002

0.55

62.0

10.0

1.4

2438

412

0.31±

0.05

0.03

8±0.

005

0.02

4±0.

002

0.67

58.9

15.8

2.0

3543

412

0.29±

0.05

0.04

5±0.

004

0.02

6±0.

001

0.80

55.6

22.0

2.4

4747

112

0.27±

0.04

0.05

0±0.

003

0.02

7±0.

001

0.91

52.3

28.0

2.7

5549

812

0.25±

0.04

0.05

3±0.

003

0.02

7±0.

001

1.00

49.3

33.5

3.0

6151

713

0.26±

0.04

0.05

5±0.

003

0.02

7±0.

001

103

Tab

leB

.9:

Win

dT

unnel

Dat

afo

rSO

FC

Model

10,

AX

ID

ouble

5330

/20

Mot

or,

AP

C22

x12

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.20

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.20

62.8

6.5

0.8

936

312

0.38±

0.06

0.02

4±0.

008

0.02

3±0.

003

0.32

59.1

13.4

1.4

2344

312

0.31±

0.05

0.03

9±0.

005

0.02

7±0.

002

0.45

53.4

24.3

2.1

4051

913

0.27±

0.04

0.05

0±0.

004

0.02

9±0.

001

0.56

47.0

35.7

2.5

4956

513

0.25±

0.04

0.05

2±0.

003

0.03

0±0.

001

0.67

41.8

45.2

2.8

5659

013

0.24±

0.04

0.05

4±0.

003

0.03

0±0.

001

0.79

36.4

55.1

3.0

6060

212

0.23±

0.04

0.05

5±0.

003

0.03

1±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.20

62.8

6.5

0.8

1136

212

0.36±

0.06

0.02

8±0.

008

0.02

3±0.

003

0.31

59.1

13.4

1.4

2444

311

0.28±

0.05

0.04

2±0.

005

0.02

7±0.

002

0.44

53.2

24.0

2.1

4151

812

0.26±

0.04

0.05

2±0.

004

0.02

9±0.

001

0.56

47.0

35.7

2.5

5156

712

0.24±

0.04

0.05

3±0.

003

0.03

0±0.

001

0.67

41.9

45.3

2.8

5759

012

0.23±

0.04

0.05

5±0.

003

0.03

1±0.

001

0.80

36.5

54.9

2.9

6160

212

0.23±

0.04

0.05

7±0.

003

0.03

1±0.

001

104

Tab

leB

.10:

Win

dT

unnel

Dat

afo

rSO

FC

Model

10,

AX

ID

ouble

5345

/14

Mot

or,

AP

C27

x13

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.18

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.24

62.7

6.9

1.1

1729

713

0.41±

0.06

0.02

9±0.

005

0.01

8±0.

002

0.33

57.8

16.3

2.0

3436

713

0.33±

0.05

0.03

8±0.

003

0.02

1±0.

001

0.42

53.1

24.8

2.7

4640

713

0.30±

0.04

0.04

2±0.

003

0.02

2±0.

001

0.53

46.2

37.3

3.2

5943

714

0.29±

0.04

0.04

7±0.

002

0.02

3±0.

001

0.62

40.6

47.5

3.5

6545

013

0.26±

0.04

0.04

8±0.

002

0.02

4±0.

001

0.71

36.5

55.0

3.6

6745

614

0.28±

0.04

0.04

9±0.

002

0.02

4±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.24

62.7

6.9

1.1

1729

813

0.39±

0.06

0.02

9±0.

005

0.01

8±0.

002

0.33

57.8

16.2

2.0

3536

813

0.32±

0.05

0.03

9±0.

003

0.02

1±0.

001

0.42

53.1

24.7

2.7

4640

513

0.30±

0.05

0.04

3±0.

003

0.02

2±0.

001

0.53

46.3

37.3

3.2

5943

713

0.27±

0.04

0.04

7±0.

002

0.02

3±0.

001

0.62

40.9

47.1

3.4

6445

014

0.28±

0.04

0.04

8±0.

002

0.02

4±0.

001

0.70

36.7

54.8

3.6

6645

713

0.25±

0.04

0.04

8±0.

002

0.02

4±0.

001

105

Tab

leB

.11:

Win

dT

unnel

Dat

afo

rSO

FC

Model

10,

AX

ID

ouble

5345

/18

Mot

or,

AP

C24

x12

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.18

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.32

63.1

6.2

0.9

1633

712

0.37±

0.06

0.03

3±0.

006

0.02

1±0.

002

0.44

59.3

13.0

1.6

3040

612

0.31±

0.05

0.04

4±0.

004

0.02

5±0.

002

0.55

54.0

23.0

2.3

4746

813

0.28±

0.04

0.05

2±0.

003

0.02

6±0.

001

0.67

49.5

31.4

2.6

5550

114

0.28±

0.04

0.05

3±0.

003

0.02

6±0.

001

0.91

40.7

47.5

3.1

6353

512

0.23±

0.04

0.05

3±0.

002

0.02

7±0.

001

1.00

37.2

54.0

3.1

6354

213

0.24±

0.04

0.05

2±0.

002

0.02

6±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.31

63.1

6.2

0.9

1733

413

0.39±

0.06

0.03

6±0.

006

0.02

1±0.

002

0.44

59.4

13.0

1.6

3040

612

0.31±

0.05

0.04

5±0.

004

0.02

4±0.

002

0.56

54.0

23.0

2.3

4846

913

0.28±

0.04

0.05

3±0.

003

0.02

6±0.

001

0.67

49.5

31.8

2.7

5650

213

0.27±

0.04

0.05

4±0.

003

0.02

6±0.

001

0.79

44.6

40.3

3.0

6052

413

0.25±

0.04

0.05

3±0.

003

0.02

7±0.

001

0.91

40.7

47.6

3.1

6353

613

0.24±

0.04

0.05

3±0.

002

0.02

7±0.

001

1.00

37.2

54.0

3.2

6554

213

0.25±

0.04

0.05

4±0.

002

0.02

7±0.

001

106

Tab

leB

.12:

Win

dT

unnel

Dat

afo

rSO

FC

Model

10,

AX

ID

ouble

5360

/20

Mot

or,

AP

C26

x15

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.20

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.43

62.2

7.9

1.4

1829

513

0.41±

0.06

0.03

5±0.

006

0.02

7±0.

002

0.55

58.4

14.8

2.2

3035

113

0.36±

0.05

0.04

2±0.

004

0.02

9±0.

001

0.63

54.7

21.7

2.7

4238

514

0.34±

0.05

0.04

8±0.

004

0.03

0±0.

001

0.80

50.6

29.2

3.2

5141

413

0.30±

0.05

0.05

2±0.

003

0.03

1±0.

001

0.93

46.1

37.5

3.6

5943

214

0.30±

0.04

0.05

5±0.

003

0.03

1±0.

001

1.00

43.7

41.8

3.7

6244

014

0.30±

0.04

0.05

6±0.

003

0.03

2±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.42

62.2

7.9

1.4

1829

512

0.38±

0.06

0.03

6±0.

006

0.02

7±0.

002

0.55

58.5

14.5

2.2

3035

113

0.36±

0.05

0.04

2±0.

004

0.02

9±0.

001

0.68

54.7

21.6

2.7

4238

513

0.31±

0.05

0.04

9±0.

004

0.03

0±0.

001

0.80

50.6

29.0

3.2

5241

313

0.30±

0.05

0.05

3±0.

003

0.03

1±0.

001

0.89

47.0

35.8

3.5

5942

913

0.28±

0.04

0.05

5±0.

003

0.03

1±0.

001

1.00

43.7

41.8

3.7

6344

013

0.29±

0.04

0.05

7±0.

003

0.03

2±0.

001

107

Tab

leB

.13:

Win

dT

unnel

Dat

afo

rSO

FC

Model

11,

AX

ID

ouble

5330

/20

Mot

or,

AP

C24

x12

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.20

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.21

63.7

7.5

1.1

1434

312

0.37±

0.06

0.02

8±0.

006

0.02

3±0.

002

0.32

59.3

15.8

1.7

2642

113

0.31±

0.05

0.03

5±0.

004

0.02

4±0.

001

0.56

44.7

42.5

3.1

4952

713

0.26±

0.04

0.04

2±0.

003

0.02

8±0.

001

0.67

38.8

53.3

3.4

6354

213

0.25±

0.04

0.05

1±0.

002

0.02

8±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.20

64.1

6.8

1.0

1534

012

0.35±

0.06

0.03

2±0.

006

0.02

2±0.

002

0.31

59.3

15.7

1.8

2842

012

0.29±

0.05

0.03

8±0.

004

0.02

6±0.

001

0.44

51.9

29.3

2.6

4349

112

0.26±

0.04

0.04

3±0.

003

0.02

7±0.

001

0.56

44.8

42.5

3.2

5852

812

0.24±

0.04

0.05

0±0.

003

0.02

8±0.

001

0.67

38.8

53.2

3.4

6454

313

0.24±

0.04

0.05

2±0.

002

0.02

8±0.

001

108

Tab

leB

.14:

Win

dT

unnel

Dat

afo

rSO

FC

Model

11,

AX

ID

ouble

5345

/14

Mot

or,

AP

C22

x12

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.17

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.24

64.7

5.8

0.8

1435

713

0.40±

0.06

0.03

8±0.

008

0.02

4±0.

003

0.34

62.0

11.0

1.3

2443

012

0.32±

0.05

0.04

4±0.

006

0.02

7±0.

002

0.46

56.0

21.9

2.0

4251

913

0.29±

0.04

0.05

4±0.

004

0.02

9±0.

001

0.59

50.1

32.7

2.5

5456

813

0.26±

0.04

0.05

8±0.

003

0.03

0±0.

001

0.70

45.0

42.0

2.6

5858

614

0.26±

0.04

0.05

9±0.

003

0.03

0±0.

001

0.83

39.4

52.5

2.9

6360

813

0.24±

0.04

0.05

9±0.

003

0.03

0±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.23

64.7

5.8

0.8

1435

612

0.39±

0.06

0.03

8±0.

008

0.02

4±0.

003

0.34

62.0

11.1

1.3

2542

913

0.35±

0.05

0.04

7±0.

006

0.02

7±0.

002

0.46

56.1

22.1

2.0

4251

814

0.30±

0.04

0.05

4±0.

004

0.02

9±0.

001

0.59

49.9

33.3

2.4

5356

012

0.24±

0.04

0.05

8±0.

003

0.03

0±0.

001

0.70

45.3

41.7

2.7

6158

912

0.22±

0.04

0.06

0±0.

003

0.03

0±0.

001

0.81

39.6

52.0

2.9

6560

813

0.23±

0.04

0.06

0±0.

003

0.03

0±0.

001

109

Tab

leB

.15:

Win

dT

unnel

Dat

afo

rSO

FC

Model

11,

AX

ID

ouble

5345

/18

Mot

or,

AP

C26

x15

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.18

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.31

63.0

9.0

1.5

2131

513

0.38±

0.06

0.03

8±0.

005

0.02

5±0.

002

0.44

57.1

20.0

2.5

4037

513

0.32±

0.05

0.04

9±0.

004

0.02

9±0.

001

0.55

51.2

31.0

3.1

5441

414

0.32±

0.05

0.05

5±0.

003

0.03

0±0.

001

0.72

43.9

44.2

3.6

6343

913

0.29±

0.04

0.05

8±0.

003

0.03

1±0.

001

0.80

40.5

50.6

3.7

6544

513

0.28±

0.04

0.05

8±0.

003

0.03

1±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.31

63.0

8.9

1.5

2330

612

0.38±

0.06

0.04

3±0.

006

0.02

6±0.

002

0.44

57.1

19.9

2.5

4137

512

0.31±

0.05

0.05

1±0.

004

0.02

9±0.

001

0.55

51.2

30.8

3.1

5541

414

0.32±

0.05

0.05

6±0.

003

0.03

0±0.

001

0.66

45.8

41.0

3.5

6243

413

0.29±

0.04

0.05

8±0.

003

0.03

1±0.

001

0.79

40.4

50.4

3.7

6744

613

0.28±

0.04

0.05

9±0.

003

0.03

1±0.

001

110

Tab

leB

.16:

Win

dT

unnel

Dat

afo

rSO

FC

Model

11,

AX

ID

ouble

5360

/20

Mot

or,

AP

C27

x13

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.20

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.43

64.0

7.1

1.3

1630

712

0.36±

0.06

0.02

5±0.

005

0.01

9±0.

002

0.55

60.4

13.7

2.1

3036

112

0.31±

0.05

0.03

4±0.

003

0.02

2±0.

001

0.67

56.5

20.9

2.7

4240

112

0.28±

0.05

0.03

9±0.

003

0.02

3±0.

001

0.80

52.3

28.6

3.2

5242

913

0.27±

0.04

0.04

2±0.

002

0.02

4±0.

001

0.90

48.8

35.2

3.5

5944

713

0.27±

0.04

0.04

4±0.

002

0.02

4±0.

001

1.00

45.4

41.4

3.7

6445

913

0.25±

0.04

0.04

5±0.

002

0.02

4±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.43

64.0

7.1

1.3

1630

613

0.38±

0.06

0.02

6±0.

005

0.01

9±0.

002

0.57

60.1

14.3

2.1

3236

713

0.32±

0.05

0.03

6±0.

003

0.02

1±0.

001

0.67

56.5

20.9

2.6

4440

113

0.29±

0.05

0.04

0±0.

003

0.02

2±0.

001

0.79

52.5

28.5

3.1

5342

913

0.27±

0.04

0.04

3±0.

002

0.02

3±0.

001

0.91

48.8

35.3

3.5

6044

713

0.27±

0.04

0.04

5±0.

002

0.02

4±0.

001

1.00

45.4

41.5

3.7

6546

013

0.26±

0.04

0.04

6±0.

002

0.02

4±0.

001

111

Tab

leB

.17:

Win

dT

unnel

Dat

afo

rSO

FC

Model

12,

AX

ID

ouble

5330

/20

Mot

or,

AP

C26

x15

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.20

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.20

55.9

6.7

1.0

1126

913

0.47±

0.07

0.02

6±0.

007

0.02

3±0.

002

0.30

52.9

17.7

2.1

2634

813

0.35±

0.05

0.03

7±0.

004

0.02

9±0.

001

0.39

49.7

29.4

3.0

4540

113

0.30±

0.05

0.04

9±0.

003

0.03

0±0.

001

0.49

45.0

46.1

3.8

6244

613

0.28±

0.04

0.05

4±0.

003

0.03

1±0.

001

0.58

40.9

61.0

4.3

7347

114

0.29±

0.04

0.05

7±0.

002

0.03

2±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.20

56.0

6.9

1.0

1126

712

0.43±

0.07

0.02

7±0.

007

0.02

4±0.

002

0.31

52.5

19.8

2.3

3336

113

0.33±

0.05

0.04

4±0.

004

0.02

9±0.

001

0.43

48.4

34.7

3.3

5242

114

0.31±

0.05

0.05

0±0.

003

0.03

1±0.

001

0.55

42.1

57.7

4.2

7346

713

0.27±

0.04

0.05

8±0.

002

0.03

2±0.

001

112

Tab

leB

.18:

Win

dT

unnel

Dat

afo

rSO

FC

Model

12,

AX

ID

ouble

5345

/14

Mot

or,

AP

C24

x12

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.19

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.21

56.7

4.2

0.6

929

312

0.43±

0.07

0.02

4±0.

008

0.01

7±0.

003

0.31

55.4

9.0

1.1

1835

413

0.37±

0.06

0.03

5±0.

006

0.02

2±0.

002

0.37

54.0

13.8

1.6

2939

813

0.33±

0.05

0.04

3±0.

004

0.02

4±0.

002

0.44

51.4

23.3

2.2

4345

912

0.27±

0.04

0.04

9±0.

003

0.02

6±0.

001

0.53

49.0

32.0

2.6

5549

613

0.26±

0.04

0.05

3±0.

003

0.02

6±0.

001

0.59

47.0

39.2

2.9

5952

013

0.26±

0.04

0.05

2±0.

003

0.02

6±0.

001

0.66

44.4

48.4

3.2

6354

313

0.24±

0.04

0.05

1±0.

002

0.02

7±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.21

56.7

4.2

0.6

1029

113

0.47±

0.07

0.02

7±0.

008

0.01

7±0.

003

0.30

55.5

8.4

1.1

1834

812

0.36±

0.06

0.03

5±0.

006

0.02

2±0.

002

0.38

54.1

13.8

1.6

3039

813

0.34±

0.05

0.04

6±0.

004

0.02

5±0.

002

0.45

52.0

21.1

2.1

4044

813

0.29±

0.05

0.04

8±0.

004

0.02

5±0.

001

0.52

49.3

30.9

2.6

5449

213

0.27±

0.04

0.05

4±0.

003

0.02

6±0.

001

0.58

47.0

39.0

2.9

6052

013

0.25±

0.04

0.05

3±0.

003

0.02

7±0.

001

0.70

44.5

48.0

3.2

6454

513

0.24±

0.04

0.05

2±0.

002

0.02

7±0.

001

113

Tab

leB

.19:

Win

dT

unnel

Dat

afo

rSO

FC

Model

12,

AX

ID

ouble

5345

/18

Mot

or,

AP

C27

x13

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.18

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.31

56.1

6.1

1.0

1328

413

0.41±

0.06

0.02

5±0.

006

0.01

7±0.

002

0.44

53.5

15.8

2.0

3236

112

0.31±

0.05

0.03

8±0.

004

0.02

1±0.

001

0.55

50.3

27.6

2.8

4941

514

0.30±

0.04

0.04

3±0.

003

0.02

3±0.

001

0.66

46.8

39.9

3.5

6445

013

0.27±

0.04

0.04

8±0.

002

0.02

4±0.

001

0.80

43.1

53.0

4.0

7647

613

0.25±

0.04

0.05

0±0.

002

0.02

4±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.31

56.1

6.1

1.0

1428

512

0.39±

0.06

0.02

6±0.

006

0.01

7±0.

002

0.43

53.5

15.7

2.0

3336

113

0.32±

0.05

0.03

8±0.

004

0.02

1±0.

001

0.56

50.2

27.5

2.8

5041

613

0.29±

0.04

0.04

3±0.

003

0.02

3±0.

001

0.67

46.8

39.9

3.5

6545

113

0.27±

0.04

0.04

8±0.

002

0.02

4±0.

001

0.80

43.2

52.9

4.0

7747

614

0.26±

0.04

0.05

1±0.

002

0.02

4±0.

001

114

Tab

leB

.20:

Win

dT

unnel

Dat

afo

rSO

FC

Model

12,

AX

ID

ouble

5360

/20

Mot

or,

AP

C22

x12

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.20

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.55

56.0

6.6

0.8

1236

213

0.39±

0.06

0.03

0±0.

008

0.02

4±0.

003

0.66

55.0

10.4

1.2

2041

712

0.33±

0.05

0.03

8±0.

006

0.02

7±0.

002

0.78

53.6

15.5

1.6

2946

712

0.28±

0.05

0.04

5±0.

005

0.02

8±0.

002

0.89

52.0

21.2

2.0

3950

912

0.27±

0.04

0.05

1±0.

004

0.03

0±0.

002

1.00

50.4

27.0

2.3

4954

213

0.26±

0.04

0.05

6±0.

003

0.03

0±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.55

56.0

6.6

0.9

1336

112

0.36±

0.06

0.03

3±0.

008

0.02

6±0.

003

0.67

54.9

10.6

1.2

2241

713

0.34±

0.05

0.04

2±0.

006

0.02

7±0.

002

0.79

53.7

15.0

1.6

3046

313

0.31±

0.05

0.04

8±0.

005

0.02

8±0.

002

0.91

52.1

21.0

2.0

4050

913

0.28±

0.04

0.05

2±0.

004

0.03

0±0.

002

1.00

50.5

26.7

2.3

4854

314

0.28±

0.04

0.05

5±0.

003

0.03

0±0.

001

115

Tab

leB

.21:

Win

dT

unnel

Dat

afo

rSO

FC

Model

13,

AX

ID

ouble

5330

/20

Mot

or,

AP

C27

x13

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.20

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.22

59.5

9.0

1.3

1331

112

0.36±

0.06

0.02

1±0.

005

0.01

8±0.

001

0.30

57.0

18.4

2.2

3237

613

0.31±

0.05

0.03

4±0.

003

0.02

1±0.

001

0.39

53.5

30.8

3.1

5143

114

0.29±

0.04

0.04

1±0.

002

0.02

3±0.

001

0.49

48.2

50.0

4.1

7148

113

0.25±

0.04

0.04

6±0.

002

0.02

4±0.

001

0.56

45.1

61.0

4.4

7950

013

0.24±

0.04

0.04

7±0.

002

0.02

4±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.20

60.2

6.6

1.1

1028

712

0.39±

0.06

0.01

8±0.

005

0.01

8±0.

002

0.31

56.8

18.9

2.2

3438

012

0.29±

0.05

0.03

5±0.

003

0.02

1±0.

001

0.39

53.7

30.4

3.1

5043

013

0.28±

0.04

0.04

0±0.

002

0.02

3±0.

001

0.49

48.3

49.8

4.0

7148

213

0.24±

0.04

0.04

6±0.

002

0.02

4±0.

001

0.56

45.1

61.0

4.4

7950

014

0.26±

0.04

0.04

7±0.

002

0.02

4±0.

001

116

Tab

leB

.22:

Win

dT

unnel

Dat

afo

rSO

FC

Model

13,

AX

ID

ouble

5345

/14

Mot

or,

AP

C26

x15

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.20

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.24

60.0

7.4

1.2

1628

113

0.43±

0.07

0.03

6±0.

007

0.02

5±0.

002

0.33

57.1

17.6

2.2

3635

713

0.34±

0.05

0.04

8±0.

004

0.02

9±0.

001

0.42

54.3

27.9

3.1

5240

713

0.31±

0.05

0.05

4±0.

003

0.03

1±0.

001

0.54

49.3

46.0

3.9

6944

913

0.27±

0.04

0.05

9±0.

003

0.03

2±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.22

60.0

7.4

1.2

1628

112

0.41±

0.07

0.03

6±0.

007

0.02

5±0.

002

0.30

58.1

14.1

1.9

3034

213

0.35±

0.06

0.04

4±0.

004

0.02

7±0.

001

0.38

55.5

23.7

2.8

4639

113

0.32±

0.05

0.05

3±0.

003

0.03

0±0.

001

0.45

53.3

31.4

3.2

5641

513

0.30±

0.05

0.05

7±0.

003

0.03

1±0.

001

0.53

49.3

45.8

3.9

7144

814

0.30±

0.04

0.06

1±0.

003

0.03

2±0.

001

117

Tab

leB

.23:

Win

dT

unnel

Dat

afo

rSO

FC

Model

13,

AX

ID

ouble

5345

/18

Mot

or,

AP

C22

x12

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.18

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.31

60.6

5.3

0.7

1334

613

0.41±

0.07

0.03

6±0.

009

0.02

3±0.

003

0.43

59.3

10.2

1.2

2342

013

0.34±

0.05

0.04

4±0.

006

0.02

6±0.

002

0.56

56.7

19.0

1.9

4150

413

0.29±

0.04

0.05

6±0.

004

0.02

9±0.

002

0.66

54.2

28.8

2.4

5455

913

0.27±

0.04

0.05

9±0.

003

0.03

0±0.

001

0.80

51.1

39.8

2.9

6560

514

0.25±

0.04

0.06

1±0.

003

0.03

1±0.

001

0.91

48.3

50.0

3.3

7463

614

0.24±

0.04

0.06

3±0.

002

0.03

2±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.31

60.6

5.3

0.7

1334

713

0.41±

0.06

0.03

8±0.

008

0.02

3±0.

003

0.43

59.2

10.2

1.2

2441

812

0.33±

0.05

0.04

8±0.

006

0.02

7±0.

002

0.56

56.7

19.4

1.9

4250

413

0.28±

0.04

0.05

6±0.

004

0.02

9±0.

002

0.66

54.2

28.7

2.4

5555

912

0.25±

0.04

0.06

1±0.

003

0.03

0±0.

001

0.80

51.1

39.7

2.9

6660

613

0.24±

0.04

0.06

2±0.

003

0.03

1±0.

001

0.89

48.2

50.0

3.3

7563

713

0.23±

0.04

0.06

4±0.

003

0.03

2±0.

001

118

Tab

leB

.24:

Win

dT

unnel

Dat

afo

rSO

FC

Model

13,

AX

ID

ouble

5360

/20

Mot

or,

AP

C24

x12

Pro

pW

ind

Tunnel

.A

irden

sity

,ρ

was

mea

sure

dto

be

1.20

kg/

m3

(a)

Wit

hout

Fuse

lage

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.44

60.7

5.0

0.8

1031

313

0.43±

0.07

0.02

5±0.

007

0.02

1±0.

002

0.55

59.5

9.2

1.3

2137

214

0.38±

0.06

0.03

6±0.

005

0.02

4±0.

002

0.67

57.8

15.3

1.9

3342

613

0.32±

0.05

0.04

3±0.

004

0.02

6±0.

001

0.79

55.9

22.2

2.4

4447

314

0.30±

0.04

0.04

7±0.

003

0.02

7±0.

001

0.90

54.0

29.5

2.9

5850

913

0.26±

0.04

0.05

3±0.

003

0.02

7±0.

001

1.00

51.9

36.8

3.3

6653

913

0.25±

0.04

0.05

4±0.

002

0.02

8±0.

001

(b)

Wit

hFu

sela

ge

DVc

(V)

I c(A

)τ

(N-m

)T

(N)

ω(r

ad/s

)S

(m/s

)J

CT

CP

0.43

60.7

5.0

0.8

1231

213

0.42±

0.07

0.03

1±0.

007

0.02

1±0.

002

0.55

59.5

9.4

1.4

2237

212

0.34±

0.06

0.03

8±0.

005

0.02

4±0.

002

0.67

57.8

15.2

1.9

3342

612

0.29±

0.05

0.04

3±0.

004

0.02

6±0.

001

0.80

55.9

22.4

2.5

4847

313

0.28±

0.04

0.05

1±0.

003

0.02

7±0.

001

0.91

53.9

29.6

2.9

6051

013

0.26±

0.04

0.05

5±0.

003

0.02

8±0.

001

1.00

52.0

36.8

3.3

6853

814

0.26±

0.04

0.05

6±0.

002

0.02

8±0.

001

simulation, design and validation of a solid oxide …

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